Methicillin-resistant Staphylococcus aureus (MRSA) has often been isolated from livestock and companion animals, including horses. Seven cases of MRSA infection in Thoroughbred racehorses were observed in an equine hospital in Japan in 2020. In this study, MRSA isolates from these seven horses and nine veterinarians in the equine hospital were studied to examine their genetic relatedness and evaluate the possibility of MRSA transmission. The MRSA isolates were subjected to whole-genome sequencing for multi-locus sequence typing, S. aureus protein A (spa) typing, staphylococcal cassette chromosome typing, and antimicrobial resistance gene detection. Minimum inhibitory concentrations of antibiotics were assessed to determine the antimicrobial susceptibility phenotype of the isolates. Phylogenetic trees based on single nucleotide polymorphisms were constructed to identify genetically close isolates. All isolates from horses and veterinarians belonged to sequence type (ST) 1, spa type t1784, with a point mutation in gyrA and double point mutations in grlA, which is known to cause fluoroquinolone resistance. All ST1-t1784 isolates were genetically closely related based on the phylogenetic tree. Our results suggested an outbreak and horse–veterinarian transmission of ST1-t1784 strains in an equine hospital.