The evolution of reproductive barriers is fundamental to the formation of new species and can help us understand the diversification of life on Earth. These reproductive barriers often take the form of hybrid incompatibilities, where genes derived from two different species no longer interact properly. Theory predicts that incompatibilities involving multiple genes should be common and that rapidly evolving genes will be more likely to cause incompatibilities, but empirical evidence has lagged behind these predictions. Here, we describe a mitonuclear incompatibility involving three genes within respiratory Complex I in naturally hybridizing swordtail fish. Individuals with specific mismatched protein combinations fail to complete embryonic development while those heterozygous for the incompatibility have reduced function of Complex I and unbalanced representation of parental alleles in the mitochondrial proteome. We localize the protein-protein interactions that underlie the incompatibility and document accelerated evolution and introgression in the genes involved. This work thus provides a precise characterization of the genetic architecture, physiological impacts, and evolutionary origin of a multi-gene incompatibility impacting naturally hybridizing species.