The Scotland international fell down with apparently no one around him during the second half of the game at Select Car Leasing Stadium, raising huge concerns among players, coaches and fans.
Fleck received extensive medical treatment and was then transported on a stretcher to a waiting ambulance after being helped up with an oxygen mask.
After the game, Sheffield United boss Slavisa Jokanovic confirmed the 30-year-old was conscious and speaking in hospital, with a further update expected on Wednesday morning.
Jokanovic said: “John is conscious, he’s in the hospital, he’s talking to the doctors and he’s in good hands.
“We hope everything will be fine and we hope everything will be fine. He was speaking and he asked for the result.
“I didn’t really see the incident but it looked like he had just collapsed, with no physical contact around him.
“I am not a doctor but the news is positive. It was not an easy situation for everyone.”
Of the Fleck incident, Reading manager Veljko Paunovic said: “The experience we all had tonight was so dramatic and so horrible.
“I hope John will come back as soon as possible in great shape in his normal life, and to play football like he did before.
“I hope there will be no other consequences [for him] after that.”
Sheffield United won the game 1-0 thanks to a Jayden Bogle effort in the second half.