It brought condemnation from Tory MPs, with party chairman Brandon Lewis urging him to either "apologise or clarify" what he had mouthed.
Health Secretary Matt Hancock wrote on Twitter: "The mask slips".
Except Mr Corbyn's team soon rebuffed the accusation.
Tory MPs called for him to be ordered to apologise, with West Midlands MP Eddie Hughes saying the incident reflected how Parliament "must set a better example".
However, a spokesperson for the Labour leader said that Corbyn did not call the prime minister "a stupid woman" but rather muttered "stupid people" in response to the pantomime atmosphere in the House of Commons.
"The problem for the leader of the Labour Party is that he does not want an immediate motion of no confidence because if, as is likely it was lost, he'd be forced by his party to go for a referendum, so they're playing games".
"I can not be expected to pronounce upon that which I did not see and which was not witnessed by my advisers, and which I did not hear and which was not witnessed by my advisers".
Ex-Norwich City footballer Darren Huckerby added: 'If you are gonna blatantly lie when 20 million people have seen you say it, what else are you going to lie about?'
Manchester United striker Rashford thinks inconsistency is proving costly
Find out more here. "But for sure, I hope - it is better not to say for sure - I hope some will be available but for sure some will not be available".
In reply, May had suggested Corbyn might not enjoy the support of his own lawmakers over the European Union and, taking a well-worn line from Christmas pantomimes, said: "I've got some advice for the Right Honourable Gentleman - look behind you!".
Corbyn's remark was captured by television cameras during the question-and-answer session in parliament that British leaders have to endure every Wednesday.
It has "plunged the country into a national crisis", he added.
May had lashed out at his attempt today, likening the move to a pantomime.
But she added: 'After that we need to find out where the will of Parliament is, where the majority of MPs will vote in Parliament and nothing should be off the table, we should consider all options'.
Lowe, who also starred in Parks and Recreation, said: "I saw Jeremy Corbin call the Prime Minister a 'stupid woman" with my own eyes watching on Sky News'.
Mr Corbyn had already left the Common chamber by the time the points of order were raised and his spokesman later said he had not said anything that required an apology. She knows that perfectly well, which is why it's cynical.
Corbyn attacked May for authorising the ramping up of no deal contingency planning, which he suggested was an attempt to bounce MPs into voting for her deal.