The clash at the European Parliament earlier this month between UKIP MEPs Steven Woolfe and Mike Hookem has been reported to the French police.
European Parliament president Martin Schulz said he had referred the "regrettable" incident after a probe.
The parliament's advisory committee on conduct concluded the two men's account of events "diverged substantially".
Mr Woolfe was rushed to hospital after collapsing in the parliament later on the day of the incident.
Mr Schulz said he had referred the matter "given the seriousness of the reported facts and their possible criminal implications".
Speaking in the European Parliament in Strasbourg, Mr Schulz said medical examinations carried out following Mr Woolfe's hospital admission suggested his collapse followed a blow to the head.
He said he had taken note of Mr Woolfe's allegations, and had "no doubts about them personally".
Mr Woolfe collapsed earlier this month following an altercation with fellow MEP Mike Hookem, who has consistently denied hitting, pushing or punching Mr Woolfe.
UKIP's interim leader, Nigel Farage said there was "no evidence anybody was punched at all".
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".