He told The Sun the PM's plan would "probably kill the deal" as it would mean the US "would be dealing with the European Union" instead of with the UK.
Downing Street has not yet reacted to Mr Trump's remarks.
Theresa May has been making the case for a US free trade deal with Mr Trump, on his first UK visit as president.
She said Brexit was an "unprecedented opportunity" to create growth in the UK and US.
Mr Trump also said that former Foreign Secretary Boris Johnson - who disagrees with the PM on Brexit and resigned this week - would make a "great prime minister", adding "I think he's got what it takes".
In his interview, he also renewed his criticism of London Mayor Sadiq Khan over last year's terror attacks in London, saying he had done "a terrible job".
It comes ahead of a day of planned, and widespread, anti-Trump protests across the UK, including one in Parliament Square which involves a giant inflatable of Mr Trump as a baby. Some pro-Trump events are also taking place.
The US president and his wife, Melania, were given a red carpet reception at Blenheim Palace, Oxfordshire on Thursday evening.
They were at a black-tie dinner with Mrs May as news broke of his interview with the newspaper, which said it was conducted while he was in Brussels.
After it was published, White House spokeswoman Sarah Sanders said the president "likes and respects Prime Minister May very much", adding that he had "never said anything bad about her".
Mr Trump - who has been a long-time supporter of Brexit - told The Sun that the UK's blueprint for its post-Brexit relations with the EU was "a much different deal than the people voted on".
He said the Brexit proposals Mrs May and her cabinet thrashed out at the PM's country house Chequers last week "would probably end a major trade relationship with the United States."
"We have enough difficulty with the European Union," he said, saying the EU has "not treated the United States fairly on trading".
'I told May how to do it'
He also said Mrs May had not listened to his advice on how to do a Brexit deal, saying: "I would have done it much differently.
"I actually told Theresa May how to do it but she didn't agree, she didn't listen to me. She wanted to go a different route," he said.
Tom Newton Dunn, the Sun journalist who interviewed Mr Trump, said the US president seemed "sensitive" and knew about the "Trump baby" inflatable.
"He's really quite stung by the criticism he's been getting," said Mr Newton Dunn. "He knew all about the baby blimp. I think it hurt him."
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