The Top Gear host star called BBC head of television, Danny Cohen, to report the incident.
Producer Oisin Tymon, with whom the altercation took place, is not believed to have filed his own complaint.
Interviews are expected to be held with Jeremy Clarkson and other parties next week, and the show has been taken off-air.
Jeremy Clarkson, 54, has expressed regret over the incident, which his co-presenter James May labeled “a bit of a dust-up”.
An online petition calling for Jeremy Clarkson’s reinstatement – set up by political blogger Guido Fawkes – has accrued more than 800,000 signatures since Tuesday.
Top Gear is one of the BBC’s most popular and profitable TV shows, with an estimated global audience of 350 million.
Its success is largely attributed to Jeremy Clarkson, who has appeared on the show since 1988.
Politicians on all sides have weighed into the affair, with PM David Cameron – a friend of Jeremy Clarkson – saying he hoped the incident could be “sorted out”.
A lawyer for Oisin Tymon said his client “intends to await the outcome of the BBC investigation and will make no comment until that investigation is complete”.
Jeremy Clarkson’s approach to BBC bosses suggests he was trying to pre-empt any official complaint. The incident, at a Yorkshire hotel, is reported to have been witnessed by members of the public, as well as some of the production team.
Jeremy Clarkson was given what he called his “final warning” last May after claims he used a racist word during filming.
He later apologized for the incident which, although never broadcast, had been leaked to a tabloid newspaper.
A further incident during shooting in Argentina saw the show’s executive producer, Andy Wilman, brand 2014 an “annus horribilis” for his team.
Jeremy Clarkson, and co-presenters James May and Richard Hammond, are due to renegotiate their contracts next month.
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