It is understood that Mr Woolfe passed out after suffering what were described as two “epileptic-like fits” as well numbness on the left hand side of his body.
In his statement he made no reference to the reported altercation which took place at the European Parliament in Strasbourg.
There were unconfirmed reports that he was punched during the course of an argument while other reports suggested he hit his head after falling heavily.
A spokeswoman for French national police said that the incident had not been reported to them and they had no current plans to investigate.
“If someone decides to ring and make a complaint, we will of course follow it up,” she said.
A spokeswoman for the European Parliament confirmed Mr Woolfe had collapsed in the main building in Strasbourg, and said that an investigation into the circumstances was now under way.
UKIP leadership favourite Steven Woolfe is recovering in hospital after being admitted in a “serious” condition following an altercation at a meeting of the party’s MEPs.
The 49-year-old MEP said in a statement that a CT scan had shown that there was no blood clot on his brain but that he was being kept in hospital overnight as a precaution.
“At the moment I am feeling brighter, happier, and smiling as ever. As a precaution, I am being kept in overnight awaiting secondary tests to make sure everything in fine,” he said.
“I would like everyone to know that the parliamentary staff, the Ukip MEPs with me and hospital staff have been brilliant. Their care has been exceptional.
“I am sitting up, and said to be looking well. The only consequence at the moment is a bit of numbness on the left hand side of my face.”
Neil Hamilton, UKIP’s leader in the Welsh Assembly, said he had been told by an eyewitness that there was an argument between some MEPs.
The former Conservative MP told the BBC: “I don’t know what his current condition is. It’s obviously a serious matter if he’s been carted off to hospital with bleeding on the brain, as I understand.
“Well, this is what I’ve been told second-hand but the story has come from somebody who was an eyewitness there so you know I think it’s pretty credible.
“It’s most unfortunate but passions obviously run high.”
He added that he had been told Mr Woolfe “toppled over and hit his head on a glass window” after the confrontation, adding: “It must have been quite a wallop, I guess, to have had the impact that it seems to have had.”
Mr Hamilton admitted the incident was not a great advert for the party, but added: “Let’s not generalise it – it’s a dispute between one or two individuals. It’s not good that they are public representatives of the party in the European Parliament and that’s highly regrettable.”
UKIP MEP Roger Helmer was also at the initial meeting, where he said there was “a lively exchange of views”.
He told the BBC: “I’ve heard that he is in a serious condition, although I’ve heard that my colleague Gill Seymour, who was with him, is optimistic about his recovery.
“There were some lively exchanges of views. I think you’ll find that’s not uncommon in political meetings.
“That took place a good two hours before the voting session where I understand Steven Woolfe left.
“I certainly saw no physical altercation take place.”