The speaker said he was against the US President addressing lawmakers in Westminster Hall.
John Bercow said such a speech was "not an automatic right" and that "opposition to racism and sexism" needed to be considered, in a shock tirade that had MPs from the ruling Conservative Party accusing him of hypocrisy and disregarding his duty of neutrality.
The speaker said he was already against Trump addressing lawmakers in Westminster Hall, and that he was "even more strongly opposed" in the wake of the president's travel ban on visitors from seven Muslim-majority countries.
But Conservative MP Nadhim Zahawi, who has been critical of Trump's travel ban, said the fact that the speaker had become the story was "a bad place to be".
He pointed out that the speaker had welcomed Chinese president Xi Jinping, despite human rights concerns, and the emir of Kuwait, which bans British dual nationals of Israeli origin, to speak in parliament.
"I am against the travel ban... but it's unwise to ban the legitimately-elected president of the United States of America, our closest ally, when we're trying to urge them not to shoot from the hip," he told BBC Radio 4's Today programme.
Many opposition Labour and Scottish National Party MPs applauded the speech, while Labour leader Jeremy Corbyn backed the Speaker on Twitter, calling on Prime Minister Theresa May to cancel the state visit.
However, Tory MP Crispin Blunt warned that Bercow would have to deal with "the consequences" of his comments, stressing that speakers "do not express their opinion.
"That's the entire point, otherwise they can't remain neutral and above the political fray," he said.
US Republican Congressman Joe Wilson called the comments "very disappointing" during an interview with BBC's Newsnight, saying it was "a slap at the Republican Party."
May has come under intense pressure over the invitation, which she extended while visiting the White House just hours before he announced his travel ban.
The ban has since been temporarily suspended by a federal judge.
More than 1.8 million people have signed a public petition calling on ministers to cancel Trump's visit, which MPs are due to debate later this month, although a recent poll showed that only 36 percent of Britons opposed the visit.
The date and details of the state visit are still being worked out and a spokeswoman for the speaker's office said the government had not made any request for Trump to address parliament.
But a speech to both Houses of Commons and Lords has been a feature of many previous state visits, including one by Barack Obama in 2011.
Downing Street said it was still looking forward "to welcoming the president... later this year," and that the dates and arrangements "will be worked out in due course."
More than 160 of parliament's 650 MPs have signed a parliamentary motion opposing an address by Trump, citing the travel ban and his comments on torture and women.
May on Monday told MPs that at a summit last week, she had urged her fellow European leaders to "engage patiently and constructively" with the new US administration.
Trump's criticism of the NATO military alliance and his prediction that the EU could fall apart following Britain's vote to leave has caused alarm in European capitals.