Jensen was elected to the state Senate in 2016 from a district covering part of Carver County, Minnesota, on the outskirts of the Minneapolis-Saint Paul metropolitan area.

[1] In 2021, Jensen announced his bid to challenge incumbent Democratic governor Tim Walz in the 2022 Minnesota gubernatorial election.

[3] He attended Luther Northwestern Theological Seminary from 1977 to 1978 and the University of Minnesota, graduating with a Bachelor of Arts in physiology in 1978 and a Doctor of Medicine in 1981.

[13][14] Jensen supported a bill to allow local governments to adopt ranked-choice voting, a system some Republicans had attempted to prohibit in the state.

[2] He put forward a bill to regulate pharmacy benefit managers,[2] and to create a new commission to probe drug price increases.

[10] In January 2021, just after he retired from the State Senate, Jensen was viewed as a potential Republican candidate for governor in the 2022 election, challenging Democratic incumbent Tim Walz, and said he planned to decide whether to run in the coming months.

[18] He took an early polling and fundraising lead among Republican candidates in the primary,[4] running against former Senate Majority Leader Paul Gazelka, Lexington Mayor Mike Murphy, and others.

[23] Simon called Jensen's comments "bizarre and irresponsible" and "a cynical attempt to use extreme conspiracy theories to radicalize political supporters.

"[22] At the May 2022 Minnesota Republican convention, Jensen won the party's endorsement on the ninth round of voting among the 2,100 delegates, defeating Lexington Mayor Mike Murphy and businessman Kendall Qualls.

His fellow plaintiffs in the suit included anti-vaccine activist Simone Gold and the right-wing political organization America's Frontline Doctors (AFD).

[48] In a later interview, Jensen said he had "quietly" been a member of AFD[47] and had been unaware of the involvement of the group's founder, Gold, in the January 6 United States Capitol attack.

[47] He was banned from TikTok in April 2021 and restricted from advertising on Facebook in July 2021 for violating community guidelines barring the promotion of COVID-19 misinformation.

[51] In September 2021, he called on "ALL Minnesota citizens and businesses to participate in civil disobedience" by ignoring a Biden administration proposal to require large employers to ensure that their employees were either vaccinated against COVID-19 or took weekly COVID-19 tests.

[45][52] In 2018, Jensen proposed various gun control measures in the state legislature to expand universal background checks and require that lost or stolen firearms be reported to authorities.

[53] In 2022, Jensen said at the Republican Party convention that he had been on the "wrong side" of the issue and apologized for his past support of gun measures.

[54] In 2022, Jensen pledged that, if elected governor, he would commute the sentence of Kim Potter, a police officer convicted of killing Daunte Wright at a traffic stop in 2021.

It is necessary to gain unanimous support from the three-member Board of Pardons, consisting of the governor, the attorney general, and the Minnesota Supreme Court's chief justice.

[56] Running for Senate in 2016, Jensen expressed support for abolishing the Met Council, a regional governmental agency covering the Minneapolis–Saint Paul metropolitan area.

[61][62] In a September 2022 campaign speech, he falsely claimed that some schools provide litter boxes for children who identify as furries.