Lloris was due to join up with Didier Deschamps' France squad for qualifiers against Iceland and Turkey but Real Madrid stopper Alphonse Areola is expected to take his place in the starting XI.
"It is difficult to say exactly how long [Lloris] will not be available," Deschamps said.
"What matters to us right now is that he will not be with us for this round of games or for the next. Almost certainly, he won't be back on the pitch in 2019."
Lloris was taken off on a stretcher after a horrific-looking landing
Image credit: Getty Images
Lloris was injured falling backwards after dropping the ball on the line, allowing Neal Maupay to nod the ball home from a yard out.
Spurs went on to record their second consecutive defeat despite the efforts of substitute goalkeeper Paolo Gazzaniga and manager Mauricio Pochettino admitted that it was partly down to losing the influential Lloris.
"To concede after three minutes in the way we did and what happened to our captain, it is normal that the impact was massive for the team," Pochettino said.
"It is an emotional game and the team was very affected, we never can be in the game.
"We did not show our real performance, I am never going to take the credit away from Brighton, we need to give them the credit too, the team suffered a massive impact after three minutes.
"I feel sorry for our fans, I want to say thank you for the massive effort coming here, we know how they feel, very disappointed, everybody feels really bad, the players and staff are the same.
"We need to find a way to stay together and be all together again and find a good dynamic."