The forces driving the evolution of extra-pair reproduction in socially monogamous animals remain widely debated and unresolved. One key hypothesis is that female extra-pair reproduction evolves through indirect genetic benefits, reflecting increased additive genetic value of extra-pair offspring. Such evolution requires that a female's propensity to produce offspring that are sired by an extra-pair male is heritable. However, additive genetic variance and heritability in female extra-pair paternity (EPP) rate have not been quantified, precluding accurate estimation of the force of indirect selection. Sixteen years of comprehensive paternity and pedigree data from socially monogamous but genetically polygynandrous song sparrows (Melospiza melodia) showed significant additive genetic variance and heritability in the proportion of a female's offspring that was sired by an extra-pair male, constituting major components of the genetic architecture required for extra-pair reproduction to evolve through indirect additive genetic benefits. However, estimated heritabilities were moderately small (0.12 and 0.18 on the observed and underlying latent scales, respectively). The force of selection on extra-pair reproduction through indirect additive genetic benefits may consequently be relatively weak. However, the additive genetic variance and non-zero heritability observed in female EPP rate allow for multiple further genetic mechanisms to drive and constrain mating system evolution.