Marcelo Bielsa confirmed Clarke, 18, was taken ill on the bench, prompting the game to be stopped for around 10 minutes.
Clarke, who had played the first half, was given an oxygen mask before being taken to the dressing room — where he felt better — and then hospital.
Play was halted on 82 minutes with Middlesbrough 1-0 up and the incident led to 12 minutes of injury time being added.
And during that time Bielsa's side found an equaliser through Kalvin Philips.
Bielsa said: "What we know is that he didn't feel well.
"We don't know the reasons yet.
"But when he was taken to the dressing room he was better.
The player is responsive and attending hospital with the club’s head of medicine and performance.
"He was taken to hospital to see if he is alright."
Promising wide man Clarke, who can play on the left or right, has also been eyed by Pep Guardiola's Manchester City, such is the esteem he is held in at Elland Road.
A club statement said: "Jack Clarke began to feel unwell during the second half of our Sky Bet Championship fixture with Middlesbrough and received medical attention.
"The player is responsive and attending hospital with the club’s head of medicine and performance.
"On behalf of everyone at Leeds United, we would like to thank the medical staff from both clubs for their response to the incident."
Leeds remain top of the Championship by a point with second-placed Norwich due to play rivals Ipswich on Sunday in the Old Farm Derby.
Boro boss Tony Pulis added: "I hope he is OK. Fingers crossed that he recovers because he is a very, very talented young player.
"All our thoughts from Middlesbrough Football Club go to the lad.
"I was told straight away that something had happened and I got the fourth official to speak to the referee. I thought it was important that the ref knew that this was going on.
"Fingers crossed everything will be OK with Jack."
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