The 18-year-old suffered the injury against Brighton in a 2-2 draw, which will end his season.
He went through an exploratory surgery, with the possibility he will need another operation soon.
Hudson-Odoi went on Twitter to tell the fans about his condition. He tweeted: "Operation was successful. Thank God always and thank you all for your messages and support, the return begins now."
The youngster is out of contract at the end of the next season, but the injury means that any summer transfer is very unlikely.
Opperation was Successful, Thank God always and thank you all for your messages and support,the return begins now!!! pic.twitter.com/14qw4rgRK2
— Callum Hudson-Odoi (@Calteck10) April 24, 2019