The present longitudinal study investigated the hypothesis that early musical skills (as measured by melodic and rhythmic perception and memory) predict later literacy development via a mediating effect of phonology. We examined 130 French-speaking children, 31 of whom with a familial risk for developmental dyslexia (DD). Their abilities in the three domains were assessed longitudinally with a comprehensive battery of behavioral tests in kindergarten, first grade, and second grade. Using a structural equation modeling approach, we examined potential longitudinal effects from music to literacy via phonology. We then investigated how familial risk for DD may influence these relationships by testing whether atypical music processing is a risk factor for DD. Results showed that children with a familial risk for DD consistently underperformed children without familial risk in music, phonology, and literacy. A small effect of musical ability on literacy via phonology was observed, but may have been induced by differences in stability across domains over time. Furthermore, early musical skills did not add significant predictive power to later literacy difficulties beyond phonological skills and family risk status. These findings are consistent with the idea that certain key auditory skills are shared between music and speech processing, and between DD and congenital amusia. However, they do not support the notion that music perception and memory skills can serve as a reliable early marker of DD, nor as a valuable target for reading remediation.