Growing up, Mathias supported Barcelona. His favourite players are Zinedine Zidane and Andres Iniesta. His inspiration is his children. Mathias has always aimed to be a professional football player and did not have a plan b! Outside of football, Mathias also plays padel tennis. His favourite video game is Crash Bandicoot. He enjoys watching The Intouchables and the Danish TV series Kloun. His favourite foods include steak, fries and béarnaise sauce. In the future, Mathias wants to become a decent golfer!

Jensen is a product of the Nordsjælland academy and made his debut for Denmark's senior team in 2020.

A midfielder, Jensen progressed through the academy at Nordsjælland and signed a three-year professional contract in January 2015. He was promoted into the first team squad for the 2015–16 season and made five appearances during the campaign, scoring one goal, which came in a 2–2 draw with Randers. Jensen was a regular in the 2016–17 season, making 22 appearances, before 2017–18 proved to be his breakthrough season. He made 36 appearances, scored 12 goals, was awarded the captaincy and his achievements were recognised by the DBU and his club, with the DBU 2017 Talent of the Year and FC Nordsjælland Player of the Year awards respectively.

On 8 August 2018, Jensen moved to Spain joining La Liga club Celta Vigo on a five-year contract. During an injury-affected 2018–19 season, he made just six appearances and left the club in July 2019.

On 10 July 2019, Jensen joined Brentford on a four-year contract, with the option of an additional year, for an undisclosed fee. He made 43 appearances and scored one goal during the 2019–20 season, which ended with defeat in the 2020 Championship play-off Final. Jensen made a career high 53 appearances during the 2020–21 season and celebrated promotion to the Premier League with victory in the 2021 Championship play-off Final.

He was named in the Denmark squad for Euro 2020 and he appeared as a substitute in each of the six matches during the Danes' run to the semi-final.