The 30-year-old collided with Sergio Ramos in Spurs' impressive 3-1 Champions League defeat of Real Madrid on Wednesday and picked up a knock.
He was able to continue until the end of the match, but Deschamps left him out of his France squad on Thursday after undergoing tests, with the coach claiming Lloris will be out for a minimum of "15 days".
Spurs are yet to make an announcement on the issue, but he is fully expected to miss Sunday's match with Crystal Palace and a 15-day lay-off would make him a doubt for the short trip to Arsenal on November 18.
"Hugo injured himself yesterday," Deschamps said at a news conference.
"He underwent tests this morning that confirm a tear in his adductor.
"If Hugo had been here [in the squad] Steve Mandanda would have played a match anyway because it was important to give him one. Now he'll play at least one. After that, we'll see."
France host Wales on November 10 before travelling to take on Germany four days later.