Jeremy Clarkson, 54, allegedly punched the producer after he found out there was no food prepared after a day of filming.
The broadcaster is expected to scrap the remainder of the current Top Gear TV series.
It said Jeremy Clarkson had been suspended after what it called a “fracas” and has confirmed Sunday’s episode of Top Gear will not be shown.
It is understood the two final episodes in the series will also be dropped.
An online petition calling for the BBC to “reinstate” Jeremy Clarkson has been signed by more than 150,000 people.
It was started on March 10 by political blogger Guido Fawkes.
Jeremy Clarkson has not issued a statement, but has been joking on Twitter about movies that could replace Sunday’s show.
The Sun newspaper, in which Jeremy Clarkson writes a regular column, quotes him as saying: “I’m having a nice cold pint and waiting for this to blow over.”
It also quotes a “source close to the star” denying Jeremy Clarkson punched anyone.
The BBC had announced Clarkson’s suspension in a statement which said: “Following a fracas with a BBC producer, Jeremy Clarkson has been suspended pending an investigation.
“No one else has been suspended. Top Gear will not be broadcast this Sunday. The BBC will be making no further comment at this time.”
Jeremy Clarkson has exchanged suggestions on Twitter with Top Gear co-hosts Richard Hammond and James May about movies that could be aired in place of the Sunday’s planned episode.
The Top Gear host, who has presented the motoring show since 2002, was given what he called his “final warning” last May after claims he used a racist word during filming.
Footage leaked to the Daily Mirror appeared to show Jeremy Clarkson using a racist term while reciting the nursery rhyme Eeny, Meeny, Miny, Moe.
Jeremy Clarkson later apologized for the incident, which was never broadcast.
Top Gear‘s executive producer, Andy Wilman, described last year as an “annus horribilis” for the show.
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