Sperm function and quality are primary determinants of male reproductive performance and hence fitness. The presence of rival males has been shown to affect ejaculate and sperm traits in a wide range of taxa. However, male physiological conditions may not only affect sperm phenotypic traits but also their genetic and epigenetic signatures, affecting the fitness of the resulting offspring. We investigated the effects of male‐male competition on sperm quality using TUNEL assays and geometric morphometrics in the zebrafish, Danio rerio. We found that the sperm produced by males exposed to high male–male competition had smaller heads but larger midpiece and flagellum than sperm produced by males under low competition. Head and flagella also appeared less sensitive to the osmotic stress induced by activation with water. In addition, more sperm showed signals of DNA damage in ejaculates of males under high competition. These findings suggest that the presence of a rival male may have positive effects on sperm phenotypic traits but negative effects on sperm DNA integrity. Overall, males facing the presence of rival males may produce faster swimming and more competitive sperm but this may come at a cost for the next generation.