Chiellini, 31, was injured during last weekend's 2-0 victory at Frosinone that extended Juve's club-record winning streak to 14 league matches and is expected to be sidelined for three weeks.
Juve, who trail Napoli by two points in their quest for a fifth successive Scudetto, host Maurizio Sarri's men this weekend before five-time European champions Bayern visit Turin on February 23.
The absence of Chiellini is another blow to Juve's backline after Uruguay international Martin Caceres was ruled out for the rest of the season with an Achilles injury.