The intervention came after International Trade Secretary Liam Fox said there was "no health issue" with the controversial practice.
Dr Fox, in Washington for talks with US trade representatives, said it was "too early" to comment on the specifics of a free trade agreement.
However, asked if chlorinated chickens would be allowed, his Cabinet colleague Mr Gove told BBC Radio 4's Today programme: "No. I have made it perfectly clear, and indeed this is something on which all members of the Government are agreed, that we are not going to dilute our high animal welfare standards, or our high environmental standards, in pursuit of any trade deal."
Pressed on whether Britain would say no to a US free trade deal if America insisted on access for its farmers, the Cabinet minister said: "Yes, critically, we need to ensure that we do not compromise those standards."
Mr Gove added: "The Trade Secretary, quite rightly, pointed out that, of course, this issue is important, but we mustn't concentrate just on this one issue when we look at the huge potential that a trade deal can bring."
Earlier Dr Fox said it was "too early" to comment on the specifics of a free trade agreement.
Asked about the practice of washing poultry carcasses in chlorinated water, he said: "There is no health issue with that - the European Union has said that is perfectly safe.
"The issue lies around some of the secondary issues of animal welfare and it's perfectly reasonable for people to raise that but it will come much further down the road.
"We will want to ensure that the scientific advice that we have ensures proper protection for British consumers because dropping our standards is not the way for Britain."
His comments came after the House of Lords Energy and Environment sub-committee warned that animal welfare standards could be undermined if post-Brexit trade deals left UK farmers competing against less-regulated foreign rivals.
Meanwhile, Mr Gove insisted he favoured a "pragmatic" approach on the question of EU migrants coming to the UK in a transitional period after Brexit.
He said: "Yes, ultimately, the important point is that we are leaving, and there will be a point when we are outside the European Union, and then fully outside, master of our own destiny when we have taken back the control of our laws and of our borders.
"But, provided we know that we are going to get to that destination, then I will want to ensure that we take ... as pragmatic an approach as possible, consistent with ensuring that we have access to the talent that we need in agriculture and other areas, and that we also give business the confidence that it needs to plan."
Those comments came after Nigel Farage claimed the Tories have "sold out" their supporters and said Labour leader Jeremy Corbyn is offering a "tougher line" on free movement than the Government.
In what he described as the "great Brexit betrayal", the former Ukip leader said those who voted to leave the European Union in last year's referendum would feel "cheated" by a transitional Brexit deal.
Shadow environment secretary Sue Hayman said: "Liam Fox defended the practice of chlorine-washing chicken last night. This morning, in yet another example of Conservative chaos, Michael Gove has ruled out chlorinated chicken imports.
"This casual and inconsistent attitude towards the importing of chlorinated chicken undermines everything British poultry farmers do to produce high quality produce and uphold high animal welfare standards.
"Theresa May must put an end to the internal disarray in her Cabinet and set the record straight by publicly supporting British poultry farmers and committing to protect the British public from substandard food produce in a race-to-the-bottom Brexit.
"Labour reiterates our calls for the Government to secure the inclusion of high food and animal welfare standards in all trade agreements negotiated after Brexit."
Former Liberal Democrat leader Tim Farron said that "chicken wars" had broken out in Theresa May's Cabinet.
"The Government's post-Brexit trade negotiations are now in disarray," said Mr Farron. "The American farming lobby is hugely powerful and it might well come as news to the Americans that chlorinated chickens will not now be part of any trade deal.
"If the Government is serious about lifting Britain off the bottom of the economic growth league it should make clear that its priority is to protect trade with our biggest market, Europe, rather than trying to cobble together back-of-a-fag-packet rival agreements that will hit British living standards and British farmers."