The incident at the parliament in Strasbourg, France, came two days into a leadership contest sparked by UKIP's new leader Diane James's resignation after just 18 days as Farage's successor.
"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," Farage said in a statement.
"His condition is serious."
A picture tweeted by Britain's ITV broadcaster showed a man in a suit said to be Woolfe sprawled face down on a walkway at the glass-and-steel parliament building, with a bag and a coat next to him.
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The incident happened on Woolfe's 49th birthday.
A UKIP spokesman said Woolfe "was taken suddenly ill in the European Parliament building in Strasbourg this morning. He has been taken to hospital in the city and he is undergoing tests."
Asked whether there had been a fight, he said "we do not have that information".
The party has faced an existential crisis since pushing Britain towards a referendum on June 23 in which the country voted to quit the EU, and since Farage's resignation shortly afterwards.
James only became leader after Woolfe, her main rival, was dramatically ruled out of the contest after failing to submit his application in time.
Woolfe, who had been supported by both Farage and Arron Banks, the party's main financial backer, was quick to throw his hat into the ring to replace James on Wednesday.
However, he also admitted this week that he had considered defecting to the Conservative Party of Prime Minister Theresa May in a move that reportedly angered some colleagues.