The 18-year-old, who was substituted at half-time, was attended to by paramedics after being taken ill late in the first period.
Clarke was given oxygen by medical staff and stretchered away before being taken to James Cook University Hospital in Middlesbrough for treatment.
He was discharged in the evening but remained under the supervision of United’s medical staff overnight before being allowed home on Sunday.
United managing director Angus Kinnear said: “Jack has had messages from football fans from every club, as you can imagine, and we all really appreciate it.
“He will undergo some more tests this week and everything is looking well, but he will not train for the rest of the week.
“In the meantime, we would like to thank everyone who has sent well wishes and once again thank Middlesbrough for all they did for Jack.”
The game resumed after a break in play, with a dramatic finale seeing Kalvin Phillips level in the 11th minute of stoppage time to earn Leeds a point – and cancel out Lewis Wing’s opener.
Middlesbrough manager Tony Pulis cast aside any concern at the lengthy period of added-on time to pass on the club’s best wishes to Clarke.
Pulis said: “I was more concerened about Jack Clarke and I hope he is okay. The more important thing was making sure the boy, fingers crossed, is okay and recovers because he is a very, very talented young player.”
Head coach Marcelo Bielsa felt that his Leeds side deserved at least a point following their strong second-half display.
Bielsa, whose side welcome Swansea City on Wednesday evening, said: “In the beginning of the first half and the end of the second half, we were good. We could have won the game.
“If we take into account the 15 minutes of the first half, we were not at ease, but apart from this, I think we dominated the game, created chances and deserved to score the goal and we probably deserved to score other goals.”
Fifth-placed Boro visit Sheffield United in a key game on Wednesday evening and Pulis added: “It was disappointing because it is late and when that happens, it is always hard to take.
“Now we have a big game against Sheffield United, who are flying. It is always difficult going to Bramall Lane. It will be a tough game and we have to stand up and give it the best we possibly can.”