In a familiar Twitter outburst, the president called the actor "a very low IQ individual" before suggesting he had "received too many shots to the head by real boxers in movies."
He added: "I watched him last night and truly believe he may be 'punch-drunk'. I guess he doesn’t realise the economy is the best it’s ever been with employment being at an all time high, and many companies pouring back into our country. Wake up Punchy!"
Mr Trump did not refer to a specific film, although De Niro has appeared in a number of violent roles including 1980 boxing classic Raging Bull.
The attack came a few days after the actor used his speech at the Tony Awards to criticise the president.
"I’m gonna say one thing: f*** Trump," he told the audience at New York's Radio City Music Hall, before he introduced Bruce Springsteen.
The 74-year-old then raised both fists in the air as he received a raucous standing ovation from the audience.
He added: "It’s no longer 'down with Trump.' It’s 'f*** Trump."
De Niro followed up his speech on a visit to Toronto where he apologised for the president, but not to him.
"I just want to make a note of apology for the idiotic behaviour of my president," he said. "It's a disgrace. And I apologise to [Canadian Prime Minister] Justin Trudeau and the other people at the G7. It's disgusting."
Mr Trump usually uses Twitter to hit back at his critics within hours, but his delayed reaction to De Niro's speech is likely due to his busy schedule.
The US president has been holding talks with North Korean leader Kim Jong-un for the last two days at a summit in Singapore.
The meeting centred on nuclear disarmament and reducing tensions, and it concluded with a one-page agreement.
In the press conference afterwards, however, Mr Trump added another announcement - the cancellation of war games with South Korea.
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