Temporal and phonological predictability in children’s literature may support early literacy acquisition. Realization of predictive structure in caregiver prosody could guide children’s attention during shared reading, thereby supporting reading subskill development. However, little is known about how predictive structure is realized prosodically during child-directed reading. We investigated whether speakers use word intensity to signal predictive metric and rhyme structure in child-directed and read-alone productions of The Cat in the Hat (Dr. Seuss, 1957), by modeling maximum intensity (dB) of monosyllabic words as a function of metric strength, rhyme predictability, and a set of control parameters. In the control model, intensity increased with lower lexical frequency, capitalization, first mention, and likelihood of a syntactic boundary. Metric structure predicted word intensity beyond these control factors in a hierarchical manner: words aligned with beat one in a 6/8 metric structure were produced with highest intensity, words aligned with beat four were produced with intermediate intensity, and words aligned with all other beats were produced with the lowest intensity. Additionally, phonologically predictable rhyme targets were reduced in intensity. The effects of meter and rhyme were not moderated by the presence of a child audience. These results demonstrate that predictability along multiple dimensions is encoded during reading of poetic children’s literature, and that metric structure is realized hierarchically in word intensity. Further, the manner by which predictability is encoded in word intensity differs from that previously reported for word duration in this corpus (Breen, 2018), demonstrating that intensity and duration present nonidentical prosodic information channels.