Moschcowitz received a medical degree from Columbia University College of Physicians and Surgeons.
He spent much of his career as a pathologist at Beth Israel Medical Center in Manhattan, and was later medical director of Mount Sinai Hospital (Manhattan) and Professor of Clinical Medicine at Columbia.
In 1925 Moschcowitz described the autopsy pathology of a young female patient who died of a disease that first caused petechiae, pallor, paralysis, and coma.
When the former world chess champion José Raúl Capablanca collapsed in what would prove to be his fatal stroke, Moschcowitz arranged the ambulance to take him to Mount Sinai Hospital.
After Capablanca died the next morning, Moschcowitz was one of the three doctors who performed the full autopsy.