The injury occurred during Colwill's first training session after Chelsea's recent Club World Cup victory.
As he begins his recovery, Colwill faces a six-to-eight month rehabilitation period.
Last season, Colwill was a key player for Chelsea in the Premier League, starting 35 out of 38 matches.
Manager Enzo Maresca expressed his appreciation for Colwill's contributions, saying, "Levi has been very important to us."