MEPs Steven Woolfe and Mike Hookem have been reported to French police over their altercation in the European Parliament which led to Mr Woolfe being taken to hospital in a life-threatening condition.
The fracas in Strasbourg on October 6 led to Mr Woolfe abandoning his bid to become the Ukip party's next leader.
European Parliament president Martin Schulz said he had referred the matter to the French authorities "given the seriousness of the reported facts and their possible criminal implications".
Mr Schulz said he referred the "regrettable" incident to the authorities after a recommendation from the European Parliament's advisory committee on conduct.
He told the parliament:
(The committee) concluded that the versions of the facts given by the two members involved diverged substantially and the facts seem to have happened in the absence of direct witnesses.
Mr Woolfe abandoned his bid to become Ukip leader last week, claiming the party was "ungovernable" without Nigel Farage at the helm.
He stood by his claim that he had "received a blow" from Ukip MEP Mr Hookem during the altercation and revealed he had made a police complaint about the incident.
Mr Hookem has denied hitting the North West MEP and the fallout from the incident has continued with claims that Mr Woolfe had received warnings about "inappropriate behaviour" from senior party figures.
Mr Woolfe had been seen as frontrunner in the race to replace Diane James, whose term as Ukip leader lasted just 18 days.
The new Ukip leader will be announced on November 28, with nominations to replace Ms James closing on October 31.
Among the contenders are Suzanne Evans, Paul Nuttall and Raheem Kassam.
Also running is John Rees-Evans, who apologised this week over his controversial 2014 claim that a "homosexual donkey" tried to rape his horse, describing the comments as "playful banter".