Although music is a universal feature of human culture, little is known about its origins and functions. A prominent theory of music evolution is the sexual selection hypothesis, which proposes that music evolved as a signal of genetic quality to potential mates. The sexual selection hypothesis offers several empirically testable predictions. First, musically skilled and active individuals should have greater mating success than less-skilled individuals. Second, if musical ability functions as an indicator of genetic quality, it is expected to be associated with other traits putatively related to genetic quality. Third, associations as per the first and second predictions are expected to be at least partly due to overlapping genetic influences. We tested these predictions in a large genetically informative sample of 10,975 Swedish twin individuals aged between 27 and 54 years (M = 40.1, SD = 7.7), using musical aptitude and music achievement as measures of musical ability. To assess mating success we examined number of sex-partners, age of first intercourse, sociosexuality, and number of offspring. General intelligence, simple reaction time, and height were used to investigate relationships with traits putatively related to genetic quality. Twin modelling showed moderate genetic influences on musical aptitude for both sexes (heritability estimates were 38% for males and 51% for females). Music achievement was also moderately influenced by genetic influences in males (heritability = 57%), but the genetic influences were low and nonsignificant for females (heritability = 9%). Contrary to predictions, the majority of phenotypic associations between musical ability and music achievement with mating success were nonsignificant or significant in the other direction, with those with greater musical ability scoring lower on the measures of mating success. Genetic correlations between these measures were also nonsignificant. Most correlations of musical aptitude and music achievement with genetic quality measures were significant, including correlations with general intelligence, simple reaction time, and, in females, height (but only for aptitude). However, only the correlation between musical aptitude and general intelligence in men was significantly driven by overlapping genetic influences. Our findings provide little support for a role of sexual selection in the evolution of musical ability. Alternative explanations and limitations are discussed.