Robben, Bayern’s top scorer this season with 17 league goals, limped off after 19 minutes of the 7-0 thrashing with a pinched nerve in his thigh.
Ribery lasted an hour before he went off with a sprained ankle after scoring in the record-equalling victory that sent Bayern through to the last eight.
The club confirmed on their website that both players will miss Saturday???s trip to Werder Bremen, while Xabi Alonso will also be unavailable after picking up his fifth yellow card of the season against Hannover.
There is positive news for Bayern, though, as Thiago Alcantara has taken part in team training this week after almost a year out with a knee injury.
Philipp Lahm is also back in training after recovering from a broken ankle.
Bayern are top of the Bundesliga and will go 14 points clear if they beat in-form Werder, with second-placed Wolfsburg in action against Freiburg on Sunday.