Human newborns discriminate languages from different rhythmic classes, fail to discriminate languages from the same rhythmic class, and fail to discriminate languages when the utterances are played backwards. Recent evidence showing that cotton-top tamarins discriminate Dutch from Japanese, but not when utterances are played backwards, is compatible with the hypothesis that rhythm discrimination is based on a general perceptual mechanism inherited from a primate ancestor. The present study further explores the rhythm hypothesis for language discrimination by testing languages from the same and different rhythmic class. We find that tamarins discriminate Polish from Japanese (different rhythmic classes), fail to discriminate English and Dutch (same rhythmic class), and fail to discriminate backwards utterances from different and same rhythmic classes. These results provide further evidence that language discrimination in tamarins is facilitated by rhythmic differences between languages, and suggest that, in humans, this mechanism is unlikely to have evolved specifically for language.