Badiashile was forced off late on during last week’s 3-1 FA Cup win at Villa Park and scans have revealed he faces a spell on the prolonged sidelines.
The defender has been ruled out of Monday’s trip to Crystal Palace and is set to miss the Carabao Cup Final against Liverpool on February 25.
Losing Badiashile is a real setback for Chelsea and Mauricio Pochettino as they bid to build on their victory against Villa and find some consistency.
Badiashile partnered Axel Disasi in central defence at Villa Park and Chelsea looked much more secure at the back after Thiago Silva was dropped to the bench.
Age appears to have caught up with 39-year-old Silva in recent matches and Pochettino hoped Badiashile and Disasi could start to form a consistent centre-back partnership.
While Chelsea have lost Badiashile, they are set to be boosted by the return of Levi Colwill when they face Palace.
Colwill has missed four games due to a hamstring injury but he is back in contention for the trip to Selhurst Park and is another left-footed option who could partner Disasi.
Trevoh Chalobah, who has not played this season due to a thigh injury, is back in training and nearing a return.