Structural rearrangements like copy number variations (CNVs) in the male-specific Y chromosome (MSY) have been associated with male fertility phenotypes in human and mouse but have been sparsely studied in other mammalian species. Here we designed digital droplet PCR (ddPCR) assays for seven horse MSY multi-copy genes and SRY and evaluated their absolute copy numbers (CN) in 209 normal male horses of 22 breeds, 73 XY horses with disorders of sex development (DSD) and/or infertility, five Przewalski’s horses and two kulans. This established baseline CN for these genes in horses. The TSPY gene showed the highest CN and was the most CN variable between individuals and breeds. SRY was a single-copy gene in most horses but had two to three copies in some indigenous breeds. Since SRY is flanked by two copies of RBMY, their CNVs were interrelated and may lead to SRY-negative XY DSD. The Przewalski’s horse and kulan had one copy of SRY and RBMY. TSPY and ETSTY2 showed significant CNVs between cryptorchid and normal males (p < 0.05). No significant CNVs were observed in subfertile/infertile males. Notably, CN of TSPY and ETSTY5 differed between successive male generations and between cloned horses, indicating germline and somatic mechanisms for CNVs. We observed no correlation between MSY gene CNVs and MSY haplotypes. We conclude that the ampliconic MSY reference assembly has deficiencies and further studies with an improved MSY assembly are needed to determine selective constraints over horse MSY gene CN and their relation to stallion reproduction and male biology.