Mr Johnson, a vocal anti-Brussels campaigner, lost his cool as Andrew Gwynne failed to say if Labour wanted to keep the UK in the single market.
The Cabinet Minister said: "He doesn't have a clue about whether he wants to be in the single market or out of it."
He then pointed his finger at Mr Gwynne, Labour's head of elections and campaigns, and grilled him over the issue.
Mr Johnson said: "Do you want to be in the single market or out of it? In or out? In or out? In or out? Do you want to be in or out?"
"The most important question this country has faced in the last 50 years is whether we are going to be in the European Union or out of it.
"The British people have voted to come out. Are you saying you want to stay in the single market? You're out of the single market, are you?”
Boris Johnson raged at Labour's Andrew Gwynne over Brexit Snap election 2017: The pictures politicians may not want you to see Sat, May 27, 2017
Protests, fights and daleks, it's all happening as the politicians hit the campaign trail for the snap election
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Jeremy Corbyn during a visit to Hackney Marshes Football Pitches, to highlight Labour's manifesto commitment to ensure 5% of the Premier League's television rights income is diverted to the grassroots game, during a General Election campaign
Mr Gwynne, an ally of hard-left Mr Corbyn, hit back by telling the top Tory: "You know what our position is."
But Mr Johnson responded by frantically waving his hands and urging Sky News voters not to elect a Labour government.
He said: "Don't send Jeremy Corbyn to negotiate for us, they don't have a clue about these negotiations."
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The Foreign Secretary grilled Gwynne over the single market
Presenter Adam Boulton was forced to intervene following the extraordinary showdown between the pair, which stunned viewers.
Twitter user Grant Stanley said Mr Johnson won the battle, saying: "Gwynne squirming as if caught in quicksand."
Alex Orka also hailed the Foreign Secretary, writing: "Brilliant! Boris laying into Labour's little puppet."
Sky News presenter Adam Boulton was forced to intervene
But senior Labour politician David Lammy said Mr Johnson's performance was "unedifying" in a furious social media rant.
He added: "Foreign Secretary? God help us. What a prat. We're supposed to trust this man to represent us around the world?
"Feel bad for my mate @GwynneMP having to deal with petulant teen Boris. What will the dementia tax cap be Boris? What's the next U-turn?"