Hugo Lloris dislocated his elbow during Tottenham's 3-0 loss to Brighton.
Lloris landed awkwardly in the third minute of the match after failing to hold on to a cross.
Lloris could miss more than two months.
"It was a massive impact after three minutes. It had a massive impact on the game. To concede and lose your captain is a massive impact emotionally and for the team," said Mauricio Pochettino following the loss.