The row came during an appearance by Jeremy Corbyn at the Engineering Employers’ Federation conference in London on Tuesday.
Steph McGovern, the financial journalist and breakfast TV presenter, was chairing the event.
During his address, the veteran left-winger vowed to stop hostile takeovers of British firms by broadening the scope of public interest tests.
But the atmosphere in the room changed when Channel 4 journalist Siobhan Kennedy tried to ask him a question.
Mr Corbyn looked perplexed, saying: “I thought this was a meeting at which engineering employers got the chance to ask questions rather than the media who get lots of chances.”
She asked: “Does that mean I can’t ask a question?”
Ms McGovern then shut her down, snapping: “I’m afraid not, sorry.”
That decision was loudly cheered by business leaders in the crowd, but the journalist was left fuming.
She hit out on Twitter afterwards, writing it was “Extraordinary but true!”
The reporter said: “I was going to ask him an economic/manufacturing/mad max question!
“He should have taken one more and then moved on to the room rather than rudely shut me down before I’d opened my mouth.”
And she later tweeted Ms McGovern, saying: “Hey Steph – disappointed you let Jeremy Corbyn shut me down. You’re a journalist too.
“He can’t refuse to answer my question based on my name.
“It was a legitimate question about manufacturing and the future of the British economy.”
The host replied: I’m sorry – but you heard the crowd, they’d had enough of media questions and wanted manufacturers to get a chance.
“It wasn’t a press conference and the organisers had told me to stop media questions.
“We’d already had two by the time you said where you were from.”
Jeremy Corbyn has a history of reacting badly to questions and criticism from the press.
In July 2016, video appeared to show him being held back from a Channel Four reporter who asked him about his leadership troubles.
He also accused an ITN journalist of “harassment” later that year after she tried to quit him about holding an early election.
And just this week he lashed out at the press again following days of criticism on national frontpages over criticism of his Cold War past.
He responded by vowing to clamp down on media bosses, threatening: “The general election showed the media barons are losing their influence and social media means their bad old habits are becoming less and less relevant.
“But instead of learning these lessons they’re continuing to resort to lies and smears. Their readers, you, all of us, deserve so much better.
“Well, we’ve got news for them: change is coming.”