Sheehan plays his club hurling and football with the Éire Óg club and has enjoyed much success. After impressing in various juvenile grades he first came to promise as a dual player in the minor grades. In 2006 he won a county minor 'A' championship with the club's footballers following a victory over Blackthorns of Mitchelstown. Two years later Sheehan added a county minor 'A' championship hurling medal to his collection after defeating Erin's Own in the final. By that stage Sheehan had become a key forward on the Éire Óg's junior football team. He won a Mid Cork title that year following a one-goal victory over Dripsey. Sheehan's side later claimed the county junior championship following a 1–8 to 1–5 defeat of Ballygarvan. In 2019 he won a Cork Premier Intermediate Football Championship after his return from Australia.
Minor, Under-21 and Junior
Sheehan first played for Cork with the county's minor football team in 2007. That year he won a Munster title following a 1–16 to 2–8 defeat of Kerry. By 2008 Sheehan had made it onto the Cork minor hurling team. He quickly added a Munster title in that code to his collection following a one-point defeat of Tipperary. Sheehan subsequently joined the Cork under-21 panels in both codes. He enjoyed little success with the hurlers, however, in 2009 he won a Munster under-21 football title following a 1–9 to 2–5 defeat of Tipperary. Cork later played Down in an All-Ireland final in which little separated the sides. It took a late goal from Colm O'Driscoll to secure a 1–13 to 2–9 victory for Cork and an All-Ireland medal for Sheehan. 2009 also saw Sheehan enjoy some success with the Cork junior football team. He won a Munster title in that grade also following a 1–21 to 0–13 defeat of Clare. Sheehan, however, did not play any part in Cork's subsequent All-Ireland victory. After a quiet season in 2010, Sheehan secured a second Munster under-21 football title in 2011 following a 2–24 to 0–8 trouncing of Kerry. Cork were subsequently installed as the red-hot favourites to take the All-Ireland title once again, however, Sheehan's side were defeated by Galway.
Senior
Sheehan made his senior debut for Cork when he came on as a substitute against Dublin in a National League game in 2010. By the end of the campaign he had established himself at full-forward and went on to win a National League title with a 1–17 to 0–12 defeat of Mayo in the final. Sheehan later made his championship debut in a drawn Munster semi-final with Kerry. Cork lost the replay but qualified for the All-Ireland final by taking the scenic route through the qualifiers. Down provided the opposition and a tight game developed on a rain-soaked day. Sheehan chipped in with a point as Cork triumphed by 0–16 to 0–15. It was Sheehan's first All-Ireland winners' medal and Cork's first championship title in twenty years. In 2011 Cork retained their status as National League champions following a 0–21 to 2–14 defeat of Dublin in the final. It was Sheehan's second winners' medal in that competition. He later lined out in his first Munster final, however, Kerry retained their provincial title with a 1–15 to 1–12 victory. Sheehan's season came to an end in that game as he tore his cruciate ligament early in the second half.
International rules
He played twice for Ireland against Australia in the 2013 International Rules Series. Sheehan was awarded the Player of the Series title for his efforts in the Irish record victory.
Move to AFL
In November 2013, Sheehan signed to play Australian rules football for professional Australian Football League club Carlton, on a two-year contract from January 2014. Sheehan had previously trialled with Carlton during 2009 without signing a contract, but re-opened discussions with the club following the 2013 International Rules series. Sheehan joined fellow GAA stars Zach Tuohy of Laois and Ciarán Byrne of Louth, both at Carlton. After playing for Carlton's, the Northern Blues, for much of his first season, Sheehan made his senior debut for Carlton on 9 August 2014 against. He played the last four games of the 2014 season and won the award as Carlton's best first year player for the season. However, recurring hamstring injuries severely hampered the rest of his career, and he managed only two more senior games over the next three years before being delisted at the end of 2017.