Developmental dyslexia is typically defined as a difficulty with an individual’s command of written language, arising from deficits in phonological awareness. However, motor entrainment difficulties in non-linguistic synchronization and time-keeping tasks have also been reported. Such findings gave rise to proposals of an underlying rhythm processing deficit in dyslexia, even though to date, evidence for impaired motor entrainment with the rhythm of natural speech is rather scarce, and the role of speech rhythm in phonological awareness is unclear. The present study aimed to fill these gaps. Dyslexic adults and age-matched control participants with variable levels of previous music training completed a series of experimental tasks assessing phoneme processing, rhythm perception, and motor entrainment abilities. In a rhythm entrainment task, participants tapped along to the perceived beat of natural spoken sentences. In a phoneme processing task, participants monitored for sonorant and obstruent phonemes embedded in nonsense strings. Individual sensorimotor skills were assessed using a number of screening tests. The results lacked evidence for a motor impairment or a general motor entrainment difficulty in dyslexia, at least among adult participants of the study. Instead, the results showed that the participants’ performance in the phonemic task was predictive of their performance in the rhythmic task, but not vice versa, suggesting that atypical rhythm processing in dyslexia may be the consequence, but not the cause, of dyslexic difficulties with phoneme-level encoding. No evidence for a deficit in the entrainment to the syllable rate in dyslexic adults was found. Rather, metrically weak syllables were significantly less often at the center of rhythmic attention in dyslexic adults as compared to neurotypical controls, with an increased tendency in musically trained participants. This finding could not be explained by an auditory deficit in the processing of acoustic-prosodic cues to the rhythm structure, but it is likely to be related to the well-documented auditory short-term memory issue in dyslexia.