Rhythm perception helps young infants find structure in both speech and music. However, it remains unknown whether categorical perception of suprasegmental linguistic rhythm signaled by a co-variation of multiple acoustic cues can be modulated by prior between- (music) and within-domain (language) experience. Here we tested 6-month-old German-learning infants' ability to have a categorical perception of lexical stress, a linguistic prominence signaled through the co-variation of pitch, intensity, and duration. By measuring infants' pupil size, we find that infants as a group fail to perceive co-variation of these acoustic cues as categorical. However, at an individual level, infants with above-average exposure to music and language at home succeeded. Our results suggest that early exposure to music and infant-directed language can boost the categorical perception of prominence.