It means the American could even miss the start of the Premier League season in mid September.
Pulisic is certainly out of the team's round of 16 second leg against Bayern Munich in the UEFA Champions League.
The Blues trail the German champions 3-0 in that tie.
He will have treatment, and faces a race against time to be ready for the Premier League 2020-2021 season start.
Next term begins on September 12 in England, although Chelsea may get their first game pushed forward one or two weeks, depending on their Champions League progress.