But Conte, speaking ahead of Saturday's home clash with Crystal Palace, is adamant the 26-year-old is fit and in contention to face Roy Hodgson's Premier League strugglers.
He said: "N'Golo is fine, he trained the whole week. He's in good form, yeah he's fine."
Asked to explain what happened, the former Juventus boss added: "On Friday it was very cold and after the training session he passed out briefly in the dressing room.
"After this situation, the doctor gave him many check-ups to understand his physical condition but it was all clear.
"On Sunday he was well [and could have played] but it was right not to take risks. He's okay and every check-up is okay, is perfect."
Kante's availability will come as a huge relief to Conte, whose position continues to be questioned after four defeats in five league games have left his side fifth, five points behind fourth-placed Tottenham.
And the Italian is not expecting things to get easier against a Palace team he believes are better than their 18th place in the table suggests.
"They have lost their last two games but they deserved more against Tottenham and Manchester United," he added. "We must pay great attention. We need three points and we know very well that we are playing against a good team with talented players.
Conte says N'Golo Kante is fine, in good form and has trained all week. #CHECRY— Chelsea FC (@ChelseaFC) March 9, 2018
"Our confidence when you lose many games in a row is not simple. Our confidence is normal, we are working very well like always."
Chelsea lost the reverse fixture at Selhurst Park in October to a Palace side inspired by Wilfried Zaha, a player who may return from injury on Saturday, but Conte insisted the visitors are not just a one-man team.
"We are talking about a really good player," he said. "I remember in the first game, when we lost away, he scored and created a lot of problems.
"But I think Crystal Palace are not just Zaha. [Andros] Townsend for me is a really good player, Benteke... there are many good players in their squad. To see them in this position in the table is a bit strange."