Ukip's Raheem Kassam told ITV News "punches were thrown" in an altercation over Tory defection rumours which left Steven Woolfe in hospital.
The leadership candidate said the incident was "embarrassing" and left him worried for his party's future.
But he said he was not surprised by the incident as animosity "had been allowed to bubble without being addressed" and another verbal altercation had taken place between Ukip MEPs the day before.
Mike Hookem MEP is understood to be the politician who was involved in the alleged fight with leadership favourite Steven Woolfe.
Kassam, a former adviser of Nigel Farage, said there was a "verbal altercation" and one of the politicians asked the other to "go and settle it outside".
He said: "A couple of punches were thrown and Steven Woolfe ended up losing feeling down one side of his body."
"I can't say I'm surprised given what I've heard recently about how much animosity there is among MEPs and at the top of the party," Mr Kassam added in an interview with ITV News in Washington DC.
Despite initial concern about his condition, Mr Woolfe released a statement from his hospital bed, saying he is "feeling brighter, happier and smiling as ever" after undergoing a precautionary brain scan.
Mr Kassam and Mr Woolfe both declared they will stand for the party's leadership on Wednesday after Diane James quit just 18 days into the job.
Mr Kassam, who cancelled planned media appearances when he heard about the incident, was strongly critical of Ukip's Welsh Assembly leader Neil Hamilton after he told the BBC that Mr Woolfe had "picked a fight" and "came off worst".
"Frankly I found his comments both insulting and flippant at a time when one of our members of European Parliament was in a hospital bed... It wasn't the time for Neil to go on television to start being jokey and assigning blame."
Mr Kassam added: "He fell foul of his own narcissism."