Plant species diversity regulates the productivity(1-3) and stability(2,4) of natural ecosystems, along with their resilience to disturbance(5,6). The influence of species diversity on the productivity of agronomic systems is less clear(7-10). Plant genetic diversity is also suspected to influence ecosystem function(3,11-14), although empirical evidence is scarce. Given the large range of genotypes that can be generated per species through artificial selection, genetic diversity is a potentially important leverage of productivity in cultivated systems. Here we assess the effect of species and genetic diversity on the production and sustainable supply of livestock fodder in sown grasslands, comprising single and multispecies assemblages characterized by different levels of genetic diversity, exposed to drought and non-drought conditions. Multispecies assemblages proved more productive than monocultures when subject to drought, regardless of the number of genotypes per species present. Conversely, the temporal stability of production increased only with the number of genotypes present under both drought and non-drought conditions, and was unaffected by the number of species. We conclude that taxonomic and genetic diversity can play complementary roles when it comes to optimizing livestock fodder production in managed grasslands, and suggest that both levels of diversity should be considered in plant breeding programmes designed to boost the productivity and resilience of managed grasslands in the face of increasing environmental hazards.