Initial reports suggested that Woolfe had suffered a serious head injury.
He is believed to have been struck by party colleague Mike Hookem, Ukip’s defence spokesman.
One Tory MEP said that, if proven, Hookem’s parliamentary immunity should be lifted and he should face possible criminal charges.
The incident comes after Woolfe announced on Wednesday that he will stand as a candidate for the party's leadership after Diane James stepped down.
Speaking from hospital, Woolfe said, "The CT scan has shown that there is no blood clot in the brain. 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 is fine."
"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."
Woolfe, who celebrates his 49th birthday on Thursday, is said to have been involved in a violent row after walking out of a vote at Parliament in Strasbourg on Thursday.
A parliamentary insider told this website, “It seems there was a row between the two men in a meeting room and Woolfe took off his jacket and invited Hookem outside the room.
“They went out of the room and it was there that it seems Hookem punched Woolfe.”
Other sources say the row started when Woolfe indicated he was going to defect to the Conservatives.
Brussels-based journalist James Crisp, who was in Parliament when the incident happened, tweeted, “One MEP called Woolfe a ‘joke’ and Woolfe told the MEP, ‘I have had enough of you.’”
Crisp later tweeted that it had originally been claimed Woolfe had collapsed “in an attempt to cover up the fact there had, in fact, been an altercation.”
The incident is thought to have occurred in front of ITV, a British TV camera crew.
Ukip leader Nigel Farage was later reported to be visiting Woolfe in hospital in Strasbourg.
He issued a statement which read, "I deeply regret that following an altercation that took place at a meeting of Ukip MEPs this morning that Steven Woolfe subsequently collapsed and was taken to hospital. His condition is serious."
The other candidate to have declared so far, Raheem Kassam, tweeted his best wishes for him, as did ex deputy chairwoman Suzanne Evans.
Further comment came from Tory MEP Charles Tannock who told this website, “Any violent behaviour by elected politicians as a way of setting differences is unacceptable and an appalling example to our electorates particularly younger ones.
“It is an assault on the democratic process of debate and votes. I don't agree with Stephen Woolfe on much but I wish him a speedy recovery.”
He added, “The assailant needs to be arrested and, if it is an MEP, his immunity immediately lifted by the Parliament. The police should have been invited in by President Martin Schulz to investigate.”
Tannock said, “Years ago another Ukip MEP was restrained by his colleagues when intoxicated from punching me, an incident I have never forgotten after more than a decade.”
Tory MEP Vicky Ford said, "I have many political difference with Steven but he has always been polite and chivalrous. I hope he gets better quickly. It has been very good to see MEPs from all across the political spectrum joining together to wish him a fast recovery."
Former UK Europe Minister Denis MacShane said, “Ukip is a party of hate and loathing against Europe which whipped up hate and loathing leading to violence against Poles and other European citizens in Britain after Brexit. That they descend into violence each other is no surprise. Ukip is driven by rivalry and petty jealousies. I hope Mr Wolfe survives and gets well soon to tell the world what happened. But this incident tells us all we need to know about UKIP.”
The Conservatives issued a statement saying, “Best wishes to @Steven_Woolfe and his family. We hope he makes a full and swift recovery.”
Several Tory MEPs also offered their best wishes to Woolfe in a series of tweets, including:
Jacqueline Foster said, “I'm shocked to hear the news about Stephen Woolfe MEP from Strasbourg. My thoughts are with him for a full recovery.”
Dan Hannan said “Horrified by the attack on @Steven_Woolfe, the sweetest-natured of men. We campaigned a lot together in Manchester: he charmed everyone.”
David Bannerman commented, “Alarmed to hear of collapse of @Steven_Woolfe. He's a good guy who I worked with in Ref & wish him a speedy recovery.”
Parliament’s spokesperson Jaume Duch told this website, “The only elements that we have: he collapsed on the walkway bridge in front of the chamber, was assisted by our medical services and transferred to a hospital.”
John Schranz, a spokesman for Schulz, said, “I can confirm that Woolfe collapsed outside the plenary and was taken to hospital. I myself cannot confirm the cause but Farage's statement seems quite clear to me.”