The pair were injured in Bayern's training session on Wednesday and German daily Bild claims Ribery faces a lengthy lay-off with the league leaders expected to release details on Thursday.
Ribery is reported to have suffered a muscle injury while Rafinha has damaged ligaments.
The 31-year-old Ribery missed 10 matches for the defending German champions due to a knee ligament problem at the start of the season.
Bayern are on course to claim their third straight Bundesliga title and have an 11-point lead going into the second half of the season.