MEPs Steven Woolfe and Mike Hookem have been reported to French police over their altercation at the European Parliament which plunged crisis-hit Ukip into further turmoil.
Mr Woolfe was left in hospital after the fracas in Strasbourg which led to him quitting Ukip and abandoning his bid to become the party's 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.
"It also stressed that given the seriousness of the reported facts and their possible criminal implications, further evidence is needed to clarify this matter.
"As a result I have decided to follow the recommendation of the advisory committee and I have referred this matter to the competent French authorities.
"Based on the result of the investigations I will then take a decision about a sanction to be imposed."
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 at a private meeting at the European Parliament building 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 October 6 incident has continued with claims that Mr Woolfe had received warnings about "inappropriate behaviour" from senior party figures.
Yorkshire and the Humber MEP Mr Hookem also claimed Mr Woolfe had signed in for 306 euro (£276) daily allowances at the European Parliament three times while recovering from his injuries earlier this month.
Mr Woolfe, who will sit as an independent, said last week that the incident led to him being treated by doctors for two seizures, partial paralysis and the loss of feeling in his face and body.
He insisted a blow from Mr Hookem knocked him back into the meeting room where Ukip MEPs were discussing reports that Mr Woolfe was in talks about defecting to the Conservatives.
Mr Hookem has said Mr Woolfe's political career "was over once he showed disloyalty to the Ukip party and membership when he held talks to join the Tories".
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".