The 34-year-old underwent a scan on Tuesday to ascertain the severity of the setback, which confirmed bone bruising around his left knee.
Messi missed PSG's 2-1 win away against Metz on Wednesday and the club have now confirmed that he will not be available to play on Saturday, but the Argentine is running again in training and will be assessed further over the weekend.
PSG head coach Mauricio Pochettino will be hoping that he can call upon the legendary forward for their Champions League showdown at home against Manchester City on Tuesday.
Messi has endured a frustrating start to life with the Parisian outfit since joining from Barcelona this summer, failing to score or provide an assist in any of his opening three matches this season.
PSG have also provided fitness updates regarding three more first-team players, with midfielder Marco Verratti set to resume training next week, while Sergio Ramos and Ismael Gharbi are to continue their individual training routines as they step up their recovery from respective calf and thigh injuries.