The centre-back pulled up just 30 minutes into the game at Stamford Bridge as he chased Leicester striker Jamie Vardy and was given treatement on the field before limping off.
Despite David Luiz being on the bench, Antonio Conte chose Andreas Christensen as the man to replace the England international.
Luiz recently made his Chelsea return in the 0-0 draw with Norwich City in the third round of the FA Cup having been out with a knee injury since October. Christensen has played a big role for the London side since the Brazilian's injury and played the full 90 minutes in their previous league game against Arsenal.
Blues captan Cahill has been a key player for the reigning Premier League champions this term, and his injury could force the club to look for a new centre-back in the January transfer window.
“This is football. This is life," Conte told reporters. "For sure he was our target but as you know this is football. We can have a lot of targets but you must be able to reach those targets."