The French midfielder missed Sunday's match against Premier League leaders Manchester City after the incident, which shocked teammates.
"N'Golo is fine," Conte said at his pre-match press conference. "He trained the whole week. He's in good form. He's fine.
"Last week, on Friday, it was very cold. After the training session he passed out briefly in the dressing room.
"The doctor brought him to have many check-ups, to understand his physical condition. But it was all clear. I think that on Sunday he was well, but at the same time it was right not to take a risk, to give him the opportunity not to play and to rest. He's OK. Every check-up is OK, it is perfect."
Conte said he had the option of playing either Olivier Giroud or Alvaro Morata up front against struggling Crystal Palace on Saturday. Neither started against City.
"I trust them both and for sure I'm working with them both to bring them in the best physical form and best condition," he said.
"Morata is coming (back) from a strange injury in his back. He was for a long time out. Giroud is in good form now, is working very well, is working every day and is in good physical condition. I trust a lot in all my players."
Asked about his team's confidence after four defeats in their past five Premier League matches, the Italian replied: "For sure, when you lose many games in a row it's not simple.
"We have to regret the games against Bournemouth, Watford, (Manchester) United. When you play against City there is the possibility to lose the game. Our confidence is normal. We are working very well as always."
Conte said David Luiz and Ross Barkley were injured and he had to "check a couple of situations", without going into further detail.