His announcement came as some local party members said he was "not fit to represent" them.
In a letter, the West Suffolk Conservative Association president urged Chief Whip Simon Hart not to re-admit Mr Hancock as a Tory MP.
Mr Hancock was suspended from the party for joining the I'm A Celebrity show and is currently an independent MP.
Announcing his decision not to stand at the next election, Mr Hancock said he had "discovered a whole new world of possibilities which I am excited to explore".
He added that politicians need to find "new ways to reach people" outside Parliament.
He concluded his letter by saying it had been "an honour to serve in Parliament and represent the people of West Suffolk".
"I will play my part in the debate about the future of our country and engage with the public in new ways," he said.
Mr Hancock had been a minister in successive Conservative governments since 2013 and served as health secretary during the coronavirus pandemic.
In June 2021, he was forced to resign from the role after he breached social distancing guidelines by kissing colleague, Gina Coladangelo, who later became his partner.
Despite supporting Rishi Sunak in the Conservative leadership campaign, Mr Hancock wasn't given a role in government when the prime minister entered Downing Street.
The MP subsequently joined the cast of I'm A Celebrity... Get Me Out Of Here - a decision that attracted criticism from his fellow MPs and local Conservative association, who accused him of "abandoning his constituency".
In a letter sent to Chief Whip Simon Hart on 1 December and published on the group's website on 7 December, association president Terry Wood said "a vote was taken that ruled that the Officer Group had no confidence in Matt Hancock our sitting MP, and we would request that the whip is not restored to him".
"This vote was brought about following feed-back from the constituents in West Suffolk, advising that by virtue of recent events, they consider Matt Hancock not fit to represent this constituency."
A political ally of Matt Hancock said: "This letter is irrelevant. It hasn't been sent on behalf of the Association, and the chief whip told Matt he was going to get the whip back.
"Matt had already decided not to stand again when it came to light."
Mr Hancock has previously defended his decision to appear on I'm A Celebrity saying reality TV was a "powerful tool" to reach young people.