It leaves favourite former British Foreign Secretary Boris Johnson and five other politic trailing behind him still in the contest, to succeed Theresa May at 10 Downing Street.
In the first round of voting among Conservative MPs at Westminster, Hancock came 6th with 20 votes, much fewer than Johnson with a flyaway 114 votes.
Announcing his decision, Hancock, the youngest of the politic to bid for the leadership, did not endorse any of the remaining six contenders, but instead told journalists that he was talking to all of them, Efe news reported.
In an interview in London, Hancock said: "We stand at a defining moment in our country's history and we need to deliver Brexit and then we need to cast forward and bring the country together. That's the goal."
Johnson was given a boost on Friday when he won backing from one of Britain's biggest and best known business tycoons, multimillionaire Lord Alan Sugar.
Sugar announced on his social media site that he "seriously supports Johnson to become the next British Prime Minister".
"The public like him and he will have a good chance of winning the general election in 2021 if not before," said Sugar.
In a swipe at the main opposition Labour Party and its leader, Sugar added: "Anyone who can stop Jeremy Corbyn from becoming PM has my backing."
Next week, the list is expected to shrink again when MPs hold their next rounds of voting, starting Tuesday. When only two names remain, a ballot to decide the next leader of the governing Conservatives will be held among the party's around 160,000 members across the country.
The winner will become the new Prime Minister automatically, though Queen Elizabeth still has to approve the choice.
May's failure to deliver a Brexit deal was the reason for her exit as leader of the Conservative Party. She will remain as caretaker Prime Minister until her successor is chosen.
( With inputs from IANS )