Robben lasted just 19 minutes of Bayern's 7-0 UEFA Champions League demolition of Shakhtar Donetsk on Wednesday, while Ribery hobbled off shortly before the hour.
Netherlands international Robben is suffering from a trapped nerve and Ribery has a sprained ankle, but it is as yet unclear how long either will be sidelined.
Bayern are 11 points clear of Wolfsburg at the top of the Bundesliga, and hold a 20-point advantage over third-placed Borussia Monchengladbach.
Bremen, meanwhile, are a further eight points back in eighth.
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