The 21-year-old picked up the injury in training while on loan at Championship side Birmingham City and has returned to his parent club to continue his rehabilitation.
Chong contributed two assists in 13 championship appearances for Birmingham before injury knocked on his door.
A statement on United's official website read: "Tahith has undergone surgery to repair a ruptured thigh tendon.
"The operation went well, and he will return to Manchester United to complete an expected four-to-five-month rehabilitation."
Chong added in a post on Twitter: "As a player, it hurts to be telling you guys this but, unfortunately, that's life and that's football."
"I have picked up an injury and will be out for a while. I would like to thank everyone at Birmingham City Football Club for everything they have done for me [in the] past couple of months.
"The players, staff and everyone involved has made me feel very welcoming from day one. The coach has helped me a lot and showed a lot of confidence in me, something I will not forget.
"A special mention to the fans that, from day one, have supported me in a way that has helped me massively. Focus on recovery now and coming back stronger."
Chong made his debut for the Red Devils in the FA Cup against Reading in January 2019 and has gone on to make 16 appearances for the first team in all competitions, including five in the Premier League.
He has also previously spent time on loan at Werder Bremen and Club Brugge.
