Evidence accumulates that the cerebellum’s role in the brain is not restricted to motor functions. Rather, cerebellar activity seems to be crucial for a variety of tasks that rely on precise event timing and prediction. Due to its complex structure and importance in communication, human speech requires a particularly precise and predictive coordination of neural processes to be successfully comprehended. Recent studies proposed that the cerebellum is indeed a major contributor to speech processing, but how this contribution is achieved mechanistically remains poorly understood. The current study aimed to reveal a mechanism underlying cortico-cerebellar coordination and demonstrate its speech-specificity. In a reanalysis of magnetoencephalography data, we found that activity in the cerebellum aligned to rhythmic sequences of noise-vocoded speech, irrespective of its intelligibility. We then tested whether these “entrained” responses persist, and how they interact with other brain regions, when a rhythmic stimulus stopped and temporal predictions had to be updated. We found that only intelligible speech produced sustained rhythmic responses in the cerebellum. During this “entrainment echo,” but not during rhythmic speech itself, cerebellar activity was coupled with that in the left inferior frontal gyrus, and specifically at rates corresponding to the preceding stimulus rhythm. This finding represents evidence for specific cerebellum-driven temporal predictions in speech processing and their relay to cortical regions.