2008-09: Jensen played for Herning in the Danish Under-20 league. In 28 games for that club, he scored 28 goals and added 15 assists for 43 points. Jensen played for Denmark at the 2009 Under-18 World Junior Championship (D-1B), where he picked up 1 assist in 5 games.
2009-10: Jensen played for Herning in Denmark's top league, appearing in 34 games. He scored 12 goals and added 14 assists for 26 points, good for second in scoring on his team. Jensen played in 10 playoff games for Herning, scoring 6 goals and adding 4 assists for 10 points. He was named the Rookie of the Year in the Danish League. In international play, Jensen played for Denmark on both the Under-18 and Under-20 teams. In 5 games at the U-18 D-1A tournament, Jensen scored 13 goals and added 2 assists for 15 points. He was named the Top Forward of that tournament. At the U-20 D-1A tournament, Jensen scored 3 goals and added 2 assists for 5 points in 5 games. he was also named the Top Player on his team at this tournament. Jensen was chosen eighth overall at the 2010 CHL Import Draft by the OHL's Oshawa Generals.
2010-11: Jensen joined the Oshawa Generals for his OHL rookie season, playing in 61 games for that team. He scored 29 goals and added 29 assists for 58 points, while also adding 42 penalty minutes. Jensen played for Denmark's gold medalist Under-20 team at the D-1B tournament, where he scored 2 goals and 3 assists for 5 points in 5 games. Jensen played for Team Cherry at the 2011 CHL Home Hardware Top Prospects Game.
2011-12: Signed to a three-year entry-level contract by the Canucks in September 2011, Jensen made his North American pro debut as a 19-year-old – joining Vancouver AHL affiliate Chicago in April after his second season with the OHL's Oshawa Generals. He scored 4 goals in six regular season games with the Wolves and appeared in two of five games during the playoffs; scoring 2 goals and finishing minus-two with 2 penalty minutes. He was the Generals' third-leading scorer and represented Denmark at the 2012 U20 World Junior Championship. Jensen scored 25 goals with 33 assists and was plus-two with 29 penalty minutes in 57 games for Oshawa. The Generals made the OHL playoffs after getting off to a slow start; finishing third in the East Division. Jensen scored 1 goal with 4 assists in the six-game series with Niagara. He was the leading scorer for tenth-place Denmark at the WJC, scoring 2 goals with 4 assists and was minus-13 with 4 penalty minutes.