Hugo Lloris suffered a dislocated left elbow as Tottenham lost 3-0 at Brighton on Saturday.
The France international, who won the World Cup with his country in 2018, required on-field treatment as oxygen was administered before he was taken away on a stretcher. Lloris was then transferred to a nearby hospital.
The 32-year-old underwent a series of scans and tests which revealed no fracture, and he is expected to leave hospital on Saturday night.
"We can confirm that Hugo Lloris sustained a dislocated elbow during today's match against Brighton," a Tottenham statement said.
"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.
While it is too early to put a date on his return, a source told ESPN FC that Lloris can expect to miss up to two months, possibly more. The source added that Lloris will travel to Paris on Monday to meet the France national team doctor. He will undergo another series of tests in Paris on Monday to try to determine the extent of the problem and will then return to London to start his rehabilitation.
Tottenham coach Mauricio Pochettino said after the game: "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.
"After 30 minutes it was 2-0 and we tried to find a solution, but it was impossible. It's a very difficult moment, but we need to keep going."
Lloris' injury capped a miserable afternoon for Tottenham following their embarrassing 7-2 defeat against Bayern Munich in the Champions League on Tuesday. Maupay's goal and two from Aaron Connolly meant Tottenham are still without an away league win in nine months.
Pochettino said ahead of the match that he wanted to stay for five more years at Spurs, but another defeat has cranked up the pressure on him.
"I feel very sorry for the fans. We are living in a tough moment. When we were on the top we were together, and now this movement has arrived we need to stick together," he said.
"This feeling is not so good. It is new for everyone in the club.
"Now is a moment to be strong."