Jensen played college hockey with the St. Cloud State Huskies in the NCAA Men's Division IWCHA conference. In his freshman season at St. Cloud State, Jensen recorded five goals and 18 assists in 38 games. In his sophomore season, Jensen was the third-leading scorer for St. Cloud State. Jensen recorded six goals and 26 assists in 39 games. St. Cloud State finished sixth in the competitive WCHA. After sweeping Nebraska-Omaha in the first round of the playoffs, the Huskies suffered a season-ending loss to North Dakota in the Final Five quarterfinal. In his junior season, Jensen skated in 42 games for St. Cloud State, and was named the WCHA's Defensive Player of the Year and selected to the NCAA West First All-American Team. Jensen recorded four goals and was second on the Huskies with 27 assists. St. Cloud State finished tied with Minnesota for first in the WCHA and rebounded from a loss to Wisconsin in the WCHA semifinals to reach the Frozen Four. St. Cloud State defeated Notre Dame, 5–1, and Miami, 4–1, to capture the NCAA Midwest Regional before falling to Quinnipiac, 4–1, in the Frozen Four semifinals.
On May 2, 2013, the Detroit Red Wings signed Jensen to a two-year entry-level contract. During the 2014–15 season, Jensen recorded six goals and 21 assists in 75 games for the Grand Rapids Griffins, and ranked second among Griffins defenseman in scoring. Jensen finished the season with a plus-30 rating, which was tied for the best plus-minus rating in the AHL. On July 13, 2015, the Detroit Red Wings signed Jensen to a two-year contract extension. During the 2015–16 season, on January 24, 2016, Jensen was recalled by the Detroit Red Wings. Prior to being recalled, Jensen recorded two goals and six assists in 39 games for the Grand Rapids Griffins. He was reassigned to the Griffins on January 26 without featuring in a game. On December 19, 2016, Jensen was recalled by the Detroit Red Wings. Prior to being recalled, Jensen recorded one goal and five assists in 27 games for the Grand Rapids Griffins. He made his NHL debut for the Red Wings the following day in a game against the Tampa Bay Lightning. On February 27, 2017, the Red Wings signed Jensen to a two-year contract extension. During the 2018–19 season, his third season with the Red Wings, Jensen recorded two goals and 13 assists, tying his previous season high totals through 60 games with 15 points.
Washington Capitals
While in the final year of his contract, Jensen was traded by the Red Wings, along with a fifth-round pick in the 2019 NHL Entry Draft, to the Washington Capitals in exchange for Madison Bowey, and a second-round pick in the 2020 NHL Entry Draft on February 22, 2019. He was then re-signed to a four-year, $10 million contract extension by the Capitals.
