Gerard Coyne accused Unite's current general secretary, Len McCluskey, of "dabbling in politics all the time".
Mr Coyne, the union's West Midlands secretary, launched his campaign for the top job in Birmingham.
Unite is Labour's biggest donor and Mr McCluskey has been one of leader Jeremy Corbyn's key backers in the face of opposition from some MPs.
Mr McCluskey has already announced plans to resign as general secretary but to stand again for the position, a move which brings forward the election by a year.
BBC political editor Laura Kuenssberg said Mr Coyne's challenge would be seen by the Labour leader's allies as a political attack.
She added that Mr Coyne was understood to be concerned about Mr Corbyn's anti-Trident stance given that thousands of Unite members work in the defence industry.
Announcing his candidacy on his Facebook page, Mr Coyne, who has worked for the union for more than 20 years having joined as a shop worker at Sainsbury's, said: "I believe our union needs to be changed so we can get on with the only job that matters; protecting and defending our members at work."
"We have got to be strong, smart and organised but we can't be distracted party politics.
"As a candidate, my priority is making a real difference for you rather than playing Westminster power games. It's time we changed the union to reflect our members' priorities."
Speaking after launching his campaign at Birmingham's Fort Dunlop building, Mr Coyne said: "The reality here is there's been much criticism about the fact that the general secretary and the union more generally has just been dabbling in politics all the time.
"I'm not going to fall into the trap of trying to determine who the leader of the Labour Party is.
"I am saying that actually my focus is on the members.
"It's not a political organisation, it's a trade union."
The result of the contest, which will run into next spring, will dictate who has control over a huge network of political supporters, organisation, and financial infrastructure.

The Serbian club had been banned for three seasons because of the issue.
European football's governing body Uefa said Partizan had broken rules on unpaid debts three times in the past five years.
However a Court of Arbitration for Sport statement said Partizan had provided "new evidence" to show it had paid its tax bills.
The statement added: "On this basis, the parties have agreed the exclusion imposed by (Uefa) shall be deemed to have been made conditional on the club's timely payment of the other overdue payables identified as at September 30, 2016.
"Taking into account the fact that FK Partizan has satisfied this condition, the club will be eligible to compete in future Uefa club competitions."
A new challenger to lead the UK's largest trade union says he will stop it "playing Westminster power games".
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Partizan Belgrade have had their European ban lifted after providing evidence they had cleared unpaid debts.