The Italy international underwent surgery on his left quadriceps after sustaining the injury in training earlier this week.
"The defender will continue his rehabilitation with our medical staff and is expected to rejoin the squad during pre-season," the club said in a statement.
Udogie shared pictures of himself on a hospital bed in an Instagram post on Saturday. "It doesn't take away from how grateful I am to every person that has supported me this year," he said.
Tottenham, in fifth place with 60 points, face rivals Arsenal next in the league, on April 28. Udogie made 30 appearances for Spurs this season scoring two goals and setting up three assists.
Udogie has earned three caps for the Italian national team, having made his senior debut last October. His injury could impact the reigning champions' campaign in the Euros in Germany, commencing in June.
