The USA forward will be sidelined for a number of weeks after picking up the problem in training.
Ruben Loftus-Cheek is still some way from a playing return as he continues rehabilitation from heel surgery.
Burnley are expected to be without striker Ashley Barnes for the trip to Stamford Bridge.
Barnes missed last week's FA Cup win against Peterborough and is waiting to learn the full extent of a groin problem, while midfielder Johann Berg Gudmundsson (hamstring) is unavailable.
Chelsea provisional squad: Arrizabalaga, Zouma, Christensen, Rudiger, Tomori, Emerson, James, Azpilicueta, Lamptey, Kovacic, Jorginho, Willian, Kante, Abraham, Hudson-Odoi, Mount, Batshuayi, Caballero, Gilmour, Barkley, Pedro, Giroud.
Burnley provisional squad: Pope, Bardsley, Tarkowski, Mee, Taylor, Brady Cork, Westwood, McNeil, Wood, Rodriguez, Lennon, Pieters, Hart, Lowton, Hendrick, Long, Vydra.