Ukip MEP Mike Hookem has avoided suspension from the party over the altercation which left former leadership contender Steven Woolfe in hospital.
Mr Woolfe quit the party and abandoned his leadership bid after the fracas with Mr Hookem in the European Parliament building in Strasbourg on October 6.
European Parliament president Martin Schulz has referred the "regrettable" incident to the French police "given the seriousness of the reported facts and their possible criminal implications".
Ukip has now concluded its internal inquiry into the incident and said it was "impossible" to determine what happened as there were no eye witnesses.
Party chairman Paul Oakden said he was "appalled" by the situation and revealed he "strongly considered" suspension as an option.
But he stressed that Mr Hookem apologised and showed regret for joining Mr Woolfe in the ante room where the altercation took place outside a meeting of party MEPs.
Mr Oakden also said Mr Hookem, "whilst foolish, was not the instigator of this incident or subsequent press coverage and as such cannot be held principally responsibly for either taking place".
He added: "In light of this, a formal reprimand will be placed on Mr Hookem's internal record, to be considered in the event of a re-occurrence of any infraction which might cause damage to the reputation of the party.
"Both I, and this investigation now consider this matter closed".
Commenting on the inquiry, Mr Hookem repeated his assertion that he never hit Mr Woolfe.
"It's clear from the report that Woolfe instigated the altercation," he said in a statement.
"As I have admitted, I should not have risen to the bait and gone outside the room.
"But I reiterate, I did not hit him.
"It's unfortunate that, as the report found, he fell and banged his head after falling backwards through an opened door.
"However, there is no evidence to suggest that I hit him at any time."
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 Mr Hookem during the altercation and revealed he had made a police complaint about the incident.
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".
The party inquiry blamed Mr Woolfe for instigating the altercation by suggesting he and Mr Hookem resolve the differences they were having in the MEPs meeting "man-to-man".
It said a "clear majority" of members saw Mr Woolfe remove his suit jacket "on or around the time he made the man-to-man comment" and interpreted it as an offer to Mr Hookem to go outside for a physical altercation.
The report also said Mr Hookem did not give due consideration to the party's reputation when deciding to accept Mr Woolfe's suggestion and join him in the ante room.
But it said it could not verify what then happened in the ante room outside the meeting due to the lack of witnesses, only that Mr Woolfe fell backwards through a door back into the meeting room, which was opened prior to his fall.
"The investigation cannot determine what was responsible for Mr Woolfe falling backwards through the door," it added.
Mr Oakden told BBC Radio Four's PM programme: "I didn't get the impression that anybody I was speaking to was telling me a porkie, although, clearly somebody probably was, and that is what has made this investigation so difficult to conduct.
"There is no evidence to support the claim that Mr Hookem landed a blow, a punch, on Mr Woolfe. I didn't get a sense that either of them were being untruthful.
"This is a shameful incident and both men should be embarrassed."