Musical prodigies reach exceptionally high levels of achievement before adolescence. Despite longstanding interest and fascination in musical prodigies, little is known about their psychological profile. Here we assess to what extent practice, intelligence, and personality make musical prodigies a distinct category of musician. Nineteen former or current musical prodigies (aged 12–34) were compared to 35 musicians (aged 14–37) with either an early (mean age 6) or late (mean age 10) start but similar amount of musical training, and 16 non-musicians (aged 14–34). All completed a Wechsler IQ test, the Big Five Inventory, the Autism Spectrum Quotient, the Barcelona Music Reward Questionnaire, the Dispositional Flow Scale, and a detailed history of their lifetime music practice. None of the psychological traits distinguished musical prodigies from control musicians or non-musicians except their propensity to report flow during practice. The other aspects that differentiated musical prodigies from their peers were the intensity of their practice before adolescence, and the source of their motivation when they began to play. Thus practice, by itself, does not make a prodigy. The results are compatible with multifactorial models of expertise, with prodigies lying at the high end of the continuum. In summary, prodigies are expected to present brain predispositions facilitating their success in learning an instrument, which could be amplified by their early and intense practice happening at a moment when brain plasticity is heightened.