A successful junior player, Konjuh won both the singles and doubles junior events at the Australian Open in January 2013 and, as a result, moved up to number 1 in the ITF junior world rankings. Later in the year, she also won the girls' singles event at the 2013 US Open. She turned her attention to the main tour in 2014, and in October of that year made her debut in the top 100, aged 16.
Konjuh won her first singles title on the WTA Tour at the 2015 Nottingham Open, becoming the youngest player to win a main tour event since 2006. She has also won one title on the ITF Tour.
Aged 14, Konjuh was the runner-up at the 2012 Wimbledon Championships in girls' doubles. In December 2012, Konjuh won two prestigious junior tennis tournaments, Eddie Herr and the Orange Bowl.
In January 2013, she won the singles and doubles events at the 2013 Australian Open, and became the number 1 junior in the world. She also received a call up to the Croatia Fed Cup team, where she scored the biggest win of her career, defeating Urszula Radwańska, ranked number 37 in the world, in Croatia's Fed Cup tie against Poland, at the age of 15.
In September 2013, Konjuh won the singles title at the 2013 US Open, her second singles junior Grand Slam. Despite being eligible to continue playing junior tournaments for two more years, Konjuh ceased playing junior events at the end of 2013, changing her focus to competing on the main tour in 2014.
Konjuh was awarded a main draw wild card for the 2014 ASB Classic in Auckland, New Zealand. On her debut at WTA-level, she stunned top seed and world number 14, Roberta Vinci, in the first round in three sets. It was later revealed that Konjuh has signed an exclusive deal with the ASB Classic, meaning that she will compete in the Auckland tournament for the next three years. At the 2014 Australian Open, she came through qualifying to reach her first senior Grand Slam draw, but lost in the first round to eventual champion and fourth seed Li Na.
Konjuh underwent elbow surgery on 23 January in Zagreb. Her recovery lasted four months, and she made her return in May by defeating Allie Kiick at the Open Saint-Gaudens Midi-Pyrénées. Konjuh made it to the semifinals of the $50,000 ITF tournament in France, before losing to eventual champion Danka Kovinić in straight sets. This run helped her up to a new world ranking high of number 189. Her new ranking enabled her to enter the qualifying draw at Roland Garros, but she again suffered defeat to Kovinić in the second round. She was more successful at Wimbledon, qualifying for the main draw with victories over Estrella Cabeza Candela, Laura Siegemund and Stephanie Vogt. She then earned her first career Grand Slam main draw win by defeating Marina Erakovic in the first round, and followed it up with the biggest win of her career to date, toppling former world number 12 Yanina Wickmayer in the second round. Konjuh's run came to an end in the following round, with a straight-sets loss to former world number 1, Caroline Wozniacki.
Konjuh's good form continued at the 2014 İstanbul Cup, where she came through qualifying to reach her first main draw semifinal, defeating top-40 players Magdaléna Rybáriková and Elina Svitolina en route. Her run at the event came to an end with a defeat to Roberta Vinci. Konjuh suffered disappointment at the US Open by losing to Urszula Radwańska in the first round of qualifying.
In October, Konjuh competed at the Japan Women's Open in Osaka and made the quarterfinals before losing to Zarina Diyas. The result saw her ranking climb to within the top 100 for the first time, aged just 16. She completed her year by competing in three tournaments in France, reaching the semifinals of ITF events in Poitiers and Nantes, and a quarterfinal showing at the WTA 125 tournament in Limoges. The resulting in Limoges saw Konjuh to a new career high ranking of number 84, and she completed the season ranked world number 90, and as the youngest player within the top 100.
Konjuh began her year in Auckland, comfortably defeating Mona Barthel before losing to Elena Vesnina in the second round. She lost in the first round of the 2015 Australian Open to Magdaléna Rybáriková. After a string of early losses, she qualified for the main draw of the 2015 Prague Open in April, where she defeated the seventh seed, world no. 34 Belinda Bencic of Switzerland in three sets in the first round. Konjuh then lost in the second round to wildcard Klára Koukalová. Konjuh's indifferent form continued through the clay-court season, but she earned her first main-draw win at the French Open by defeating Margarita Gasparyan, before losing to 30th seed Irina-Camelia Begu in the second round.
In June, Konjuh competed in the main draw at the inaugural Nottingham Aegon Open and reached the quarterfinals with victories over Shelby Rogers and Casey Dellacqua. After being delayed for over two days due to poor weather, Konjuh advanced to the semifinal by defeating Sachia Vickery, and later that day reached her first WTA tour final by defeating Alison Riske. Due to the poor weather conditions, the final was held back to Monday. Konjuh dropped the first set to opponent Monica Niculescu, but rebounded to earn victory and her first WTA Tour title. At the age of 17, she became the youngest player to win a main tour title since Tamira Paszek in 2006.
Ranked No. 87 in the world, Konjuh began her season at the Australian Open, where she lost in the second round to Daria Kasatkina after beating Urszula Radwańska. Except for a quarterfinal appearance at the San Antonio Open, she had early exits at most of her tournaments, including Indian Wells, Miami Open and Mutua Madrid Open (losing in the first round of the qualifying in the aforementioned events). At the French Open, Konjuh reached the second round after beating Arina Rodionova in straight sets. She then lost to No.22 seed Dominika Cibulková. After a semifinal appearance at the Bol Open, Konjuh withdrew from the Nottingham Open (where she was the defending champion) due to an injury she sustained at the previous tournament; hence, she fell from the top 100.
After early exits at the Mallorca Open and the Aegon International, Konjuh reached the second round of Wimbledon after beating Karin Knapp. She then lost to Agnieszka Radwanska in a three set thriller in which a late ankle injury halted Konjuh's chances of winning the match. After her campaign, she returned to the Top 100. Her next tournament was the 2016 Summer Olympics in Rio, where she beat Annika Beck before losing to World No.12 Carla Suárez Navarro. Despite losing in the second round of qualifying at the Western & Southern Open, Konjuh qualified for the Connecticut Open where she reached the second round by beating Kayla Day. She then played Roberta Vinci and lost in straight sets.
At the US Open, Konjuh upset 20th seed Kiki Bertens (who had previously beaten her in Miami) in the first round. She went on to beat Kurumi Nara and Varvara Lepchenko en route to her first Major fourth round where she met fourth seed Agnieszka Radwańska, whom she beat in straight sets to become the youngest US Open quarterfinalist in a decade and also the first Croatian female quarterfinalist since Karolina Šprem at Wimbledon in 2004. She lost to the tenth seed, and eventual finalist, Karolína Plíšková, in the quarter-finals in straight sets, being unable to bring up a break point on her opponent's serve. After the tournament ended, her ranking rose from 92 to 52. Despite failing in the qualifying round in both Wuhan Open and China Open, Konjuh reached the semifinals at the Guangzhou International and the quarterfinals at the Kremlin Cup, losing to Jelena Jankovic and Elina Svitolina, respectively. She ended the year as the world No. 48.
Konjuh started the year at the ASB Classic where she reached her second WTA final, beating the likes of Naomi Osaka (who retired in the first set) and Julia Görges en route. She then lost in straight sets to Lauren Davis. Despite her loss, Konjuh reached a career-high ranking of world No. 36. At the Australian Open, Konjuh beat Kristina Mladenovic in straight sets before losing to Daria Gavrilova.
After losing in the round of 16 of the St. Petersburg Ladies' Trophy to top seed Simona Halep, Konjuh played at the Dubai Tennis Championships where she beat Zhang Shuai (dropping just one game en route) in the first round. She then grabbed back-to-back upsets over No.12 seed Samantha Stosur and No.8 seed Elena Vesnina en route to the quarterfinals where she lost to No.1 seed Angelique Kerber.
At the 2017 Wimbledon Championships, she defeated world number nine Dominika Cibulková in the third round. However, she lost to the eventual finalist Venus Williams in the fourth round.