Granlund played junior ice hockey with Kärpät in 2007–08 and 2008–09, averaging greater than a point per game in both seasons, and was named a first-team All-Star by his junior A league in 2009. He gained his first professional experience late that season, making his debut with Kärpät's team in the SM-liiga on his 17th birthday. He played only two games before he became embroiled in a contract dispute with the team. Granlund and his agent alleged that the four year junior contract he signed with Kärpät in 2007 was invalid, because it failed to define what compensation he would get from the team, and that the team had altered the end date on his SM-liiga insurance application from April 2009 to April 2011 without his approval. The team admitted that mistakes were made, but that they were made in good faith as both the team and player wished to get him in their top team immediately.
Arguing his contracts to be void, and considering himself to be a free agent, Granlund signed a contract with HIFK Helsinki for the 2009–10 season; Kärpät challenged his attempts to transfer to HIFK. Granlund sued his old team in July 2009 after Kärpät failed to relent, asking a court to cancel his contracts with them and clear the way for him to play with HIFK. The two sides reached an out of court settlement a month later, allowing Granlund to transfer to his new team. He scored 13 goals and 27 assists in 43 games with HIFK in 2009–10, and was the top rookie scoring 40 points. He was named the winner of the Jarmo Wasama memorial trophy as the SM-liiga's top rookie, and with only two penalty minutes in the whole the season, he also won the Raimo Kilpiö trophy as the league's most gentlemanly player. Additionally, Granlund was voted Finland's young Athlete of the Year for 2009.
He has played with the Finnish national junior team at both the Under-18 and Under-20 World Championships in 2009 and 2010. At 2010 U18 Championship Granlund scored most assists with nine, and his total thirteen points was the third best in the tournament, as he helped Finland win its second consecutive bronze medal. At the 2010 World Junior Championship he was Finland's top scorer with seven points as the team finished fifth overall.
Among skaters Granlund was considered the top European prospect for the 2010 NHL Entry Draft by the NHL Central Scouting Bureau. While scouts have noted his small size at five feet, ten inches, they are impressed with his vision on the ice. Granlund was selected in the 2010 NHL Entry Draft, drafted ninth overall by the Minnesota Wild.
As Granlund's contract ran through the 2010–11 season, he returned to HIFK for one more season. Suffering a concussion in mid-October, Granlund was sidelined for over two months, missing the 2011 World Junior Championship as a result. Acting primarily as a playmaker, Granlund was a key player in helping HIFK win the SM-liiga title. Granlund was second in playoff scoring (5-11–16), behind team-mate Juha-Pekka Haataja (8-8--16).
Following the 2010–11 SM-liiga season, Granlund made his debut with the senior Finnish national team for the 2011 IIHF World Championship. Using the Mike Legg Michigan style scoop in a full-speed variation, Granlund scored a lacrosse style highlight reel goal in the semifinal game versus Russia, helping Finland win gold. In May 2011, Dynamo Minsk from the KHL has been publicly claiming him since the team drafted him one year prior to the NHL draft . However, because of Finland's mandatory military service requirements, Granlund remained with HIFK through the 2011–12 season. Granlund himself has stated he's not interested in playing in the KHL but planned to aim for the NHL.
Granlund signed a three-year entry level contract with the Wild during the 2012 NHL offseason. With the NHL lockout postponing the NHL season, Granlund was assigned to the Wild's American Hockey League affiliate, the Houston Aeros, to begin his 2012–13 campaign. After the lockout was lifted Granlund was recalled from Houston and made the Wild's opening night roster. In the first game back from the lockout he made his NHL debut and scored his first NHL goal, against Semyon Varlamov of the Colorado Avalanche on 19 January 2013.
Granlund's play improved during his sophomore year, scoring 8 goals and 33 assists. Midway through the season Granlund was moved to Minnesota's top line where he was frequently paired with Jason Pominville and Zach Parise.
On 21 April 2014, Granlund scored a goal in overtime to lead the Minnesota Wild to a playoff victory over the Colorado Avalanche.
In the 2014-15 NHL season Granlund again played on Minnesota's top line with Pominville and Parise, during which he would collect 8 goals and 31 assists.
The 2015-16 season saw Granlund centering the Wild's second line with a variety of wingers due to Minnesota's struggle with injuries and line shuffling. Near the end of the season, interim head coach John Torchetti placed him on the first line wing with fellow Finn Mikko Koivu, leading to a sudden uptick in points production, something Torchetti attributed to being released from the defensive duties often placed on the center position. He played very well in the Wild's short playoff run, with Torchetti calling him the Wild's "most competitive player."
On 1 August 2017, the Wild re-signed Granlund to a three-year, $17.25 million contract with an annual average of $5.75 million, avoiding arbitration.
After Granlund's "lacrosse-style" goal at the 2011 IIHF World Championship semifinal versus Russia, Finnish Hockey Mafia released the single "Taivas varjele!" featuring sampled comments by Finnish sports broadcaster Antero Mertaranta. The single released the same week of the much-talked about goal reached #2 in the Finnish Singles Chart as well as topping the chart for most Finnish Singles downloads that week.