The French international suffered a serious injury against Brighton in the Premier League on Saturday.
Lloris made a mistake that led to his side conceding the first goal in a 3-0 loss.
However, the same incident caused him to dislocate his elbow and leave the game on a stretcher, while in serious discomfort.
A Tottenham statement said: "We can confirm that Hugo Lloris sustained a dislocated elbow during today's match against Brighton.
"Our club captain was stretchered off as a result of the injury and will now return to London this evening after being assessed at a local hospital.
"Assessment will continue this coming week to ascertain the full extent of the injury and the length of time he will require to undergo rehabilitation."