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. Research Highlights 6‐month‐old German‐learning infants’ ability to perceive lexical stress prominence categorically depends on exposure to music and language at home. Infants with high exposure to music show categorical perception. Infants with high exposure to infant‐directed language show categorical perception. Co‐influence of high exposure to music and infant‐directed language may be especially beneficial for categorical perception. Early exposure to predictable rhythms boosts categorical perception of prominence.