Mark Francois has accused Michael Gove of not being a "proper Brexiteer".
The European Research Group vice-chair said he "fundamentally disagrees" with the Tory leadership contender on the issue of Brexit.
"The new Prime Minister will be a proper Brexiteer, which Michael Gove, in my opinion, is not," he told talkRADIO's Julia Hartley-Brewer.
"I will not vote for Michael Gove because it is now three years since the referendum and the British people can't be mucked about any more."
Yesterday, Mr Gove said he was "not wedded" to the October 31 Brexit deadline, and suggested he would be open to a further delay in order to secure a deal with the EU.
He told an audience in London that the delay could be a matter of weeks.
"The reason Michael Gove is doing this is because he wants the wets in the party to vote for him," Mr Francois continued.
"We now leave at Halloween. In order to protect the integrity of the democratic process we absolutely must keep to that deadline."
Ladbrokes currently have odds of 5/1 on Mr Gove becoming the next Conservative Party leader.
He has so far been publicly backed by around 28 MPs, with fellow contender Boris Johnson ahead with 42 MPs.
"There is no point flogging a dead horse," Mr Francois added.
"Go to the EU council and say the Withdrawal Agreement is dead, we want to go straight to the future relationship."