A native of Brampton, Ontario, Sean is the son of Cathy and John Monahan, and has a sister, Jacqueline. He attended St. Thomas Aquinas Secondary School. A shy child who developed into a prankster, Monahan excelled athletically. He played minor hockey and lacrosse for the Brampton Excelsiors.
Monahan played with the Mississauga Rebels. As a 15-year-old in 2010, he captained the Rebels to an OHL Cup title and was named most valuable player of the tournament. He finished the 2009–10 season with 46 goals and 40 assists in 47 games for the Rebels and was then selected by the Ottawa 67's in the first round, 16th overall, at the Ontario Hockey League (OHL) Priority Selection draft. Monahan's junior hockey career began with difficulty as he suffered a sprained wrist in his first training camp with the 67's, resulting in a slow start for him in the 2010–11 OHL season. An invitation to play in the 2011 World U-17 Hockey Challenge, in which he was a key performer for the gold medal-winning Team Ontario, allowed Monahan to regain confidence; he completed his first OHL season on the 67's second line and recorded 47 points in 65 games. Monahan played in his second international tournament following the season. He joined the Canadian Under-18 National Team for the 2011 Ivan Hlinka Memorial Tournament and scored a goal in the championship game to help Canada win a fourth consecutive gold medal at the event.
Playing alongside NHL prospects Tyler Toffoli, Shane Prince and Cody Ceci, Monahan was one of the OHL's top scorers in the 2011–12. He finished tied for 15th in league scoring with 78 points. He was named to the OHL's Second All-Star team and was the 67's representative on the league's All-Scholastic team. Monahan's third season in Ottawa was a transitional one for the franchise. The 67's had won three consecutive East Division titles between 2010 and 2012, but the graduation of top players caused the team to enter a rebuilding phase. The 67's finished in last place in the 2012–13 OHL season with just 16 wins. Monahan served as the team's captain, sharing the role with Ceci in the first half of the season until the latter player's departure in a trade. He finished the season with 31 goals and 78 points. He was invited to Team Canada's selection camp for the 2013 World Junior Ice Hockey Championships, but failed to make the team. He also missed ten games during the season after being suspended for an elbowing incident.
Monahan was one of the top-ranked prospects for the 2013 NHL Entry Draft: The NHL Central Scouting Bureau ranked him as the 5th best North American skater in its final ranking while International Scouting Services ranked him 9th overall. Among OHL draft prospects, the league's coaches rated Monahan highly for his intelligence on the ice, playmaking and stickhandling, and for his faceoff ability. He was selected in the first round, sixth overall, by the Calgary Flames. Upon his selection, the 18-year-old centre expressed his confidence that he was ready to immediately play in the NHL. He earned a spot on the Flames roster to begin the 2013–14 season and made his NHL debut on October 3, 2013, against the Washington Capitals. Monahan scored his first career point in the game, assisting on David Jones' goal in a 5–4 shootout loss. He then scored his first goal the following night against goaltender Sergei Bobrovsky of the Columbus Blue Jackets in a 4–3 win.
Though he remained eligible to return to junior without impacting his NHL contract, Monahan scored six goals in his first nine games to earn a permanent spot in Calgary. In doing so, he became the first junior-eligible player to make the full-time jump to the Flames roster since Kevin LaVallee in 33 years. Monahan scored his 20th goal in a late-season loss to the Ottawa Senators, and in doing so, became the first Flames rookie to score 20 goals since Dion Phaneuf in 2005–06 and first rookie forward since Jarome Iginla in 1996–97 to reach the mark.
On August 19, 2016, following back-to-back seasons in which he scored 60 or more points, Monahan, as a restricted free agent signed a seven-year, $44.625 million contract extension to remain in the Flames' organization through 2023.
Monahan scored his 100th career goal against Andrei Vasilevskiy of the Tampa Bay Lightning on February 23, 2017. He is the 6th youngest active player to achieve this milestone, joining the elite company of Alex Ovechkin, Sidney Crosby, Jaromír Jágr, Steven Stamkos, and Patrick Kane. His 100th goal also marked his 20th of the season, marking the 4 consecutive season he has scored at least 20 goals.
He is now the youngest Calgary Flame to reach the 100 goal milestone (22 years, 134 days), passing Joe Nieuwendyk, who was 22 years and 185 days old when he scored 100 career goals.