1. In haplodiploid social insects where males are haploid and females are diploid, inbreeding depression is expressed as the production of diploid males when homozygosity at the sex‐determining locus results in the production of diploid individuals with a male phenotype. Diploid males are often assumed to have reduced fitness compared with their haploid brothers. 2. While studying the reproductive biology of a leaf‐cutting ant, Atta sexdens, in Gamboa, Republic of Panama, we detected the presence of a larger male morph. Using microsatellite markers we were able to confirm that the large male morph was diploid in 87% of cases. 3. We infer that the Gamboa population of A. sexdens experiences inbreeding depression because diploid males were found in three out of five mature colonies. However, their frequencies were relatively low because queens were multiply mated and our estimates suggest that many diploid male larvae may not survive to adulthood. 4. We measured two traits potentially linked to male reproductive success: sperm length and sperm number, and showed that diploid males produced fewer but longer sperm. These results provide indirect evidence that diploid male reproductive success would be reduced compared with haploid males if they were able to copulate. 5. We conclude that diploid male production is likely to affect the fitness of A. sexdens queens with a matched mating, as these males are produced at the cost of workers and, if the colony survives to reach mature size, also gynes.