The Chancellor slammed his Cabinet colleague at a subcommittee over disputed assertions made by the Leave campaign that £350million sent to Brussels each week could be sent to the NHS.
Mr Hammond, who has previously faced accusations of trying to undermine the Brexit process, unleashed an angry tirade against Mr Gove, a leading figure in the Leave campaign.
The dispute is said to have taken place during a discussion on how to boost trade once Britain exits the bloc.
Mr Gove told the meeting that the referendum result proved Government-led campaigns were not succeeding.
But Mr Hammond shot back that people had voted to leave because of their “misleading” claims over EU cash, The Sun reported.
A source told the paper: “Hammond absolutely went for him.”
The latest bout of Tory in-fighting risks casting a shadow over her hard fought withdrawal terms, which EU leaders yesterday agreed meant talks could finally move on to trade.
It comes after party rebels subjected Theresa May to a Commons defeat last week, successfully demanding a “meaningful vote” on the final Brexit deal.
But Mrs May looked to have seen off another damaging defeat today after reaching a compromise over plans to write the date Britain leaves the bloc into law.
Behind-the-scenes efforts to prevent a revolt appeared to have resulted in a situation which will see March 29 2019 written into the Government’s Brexit legislation as the Prime Minister promised.
However, it will now have the added flexibility of allowing the date to be changed if negotiations with Brussels look set to stretch beyond that date.
Rebels who helped inflict Mrs May’s first Commons defeat on Wednesday lined up behind the compromise, which has been put forward by prominent backbenchers on both sides of the EU referendum divide.
The Government is understood to be “looking closely” at the amendment tabled by MPs including Remain supporter Sir Oliver Letwin and Brexiteer Bernard Jenkin – which would give ministers flexibility to change the departure day if Parliament agrees.
The Government has not formally supported the move but it would appear certain to back the measure if it presented a way for Mrs May to avoid another Commons reverse.
Former Cabinet minister Nicky Morgan, one of the rebels who helped inflict Mrs May’s first Commons defeat on Wednesday, gave her support to the compromise over the Brexit date.
She said the new amendment “demonstrates how all Conservative MPs can work together” to deliver the best possible Brexit and reflects the flexibility within the Article 50 withdrawal process.
The amendment also emphasises that “Parliament will be fully involved in Brexit”, she said.
But a senior Leave-supporting Tory said the rebels had now accepted that Government ministers are in control of setting the Brexit date.