No, but There are many types of medical or health care masters degrees in the United states, such as a master of science in epidemiology or public health or tropical medicine or a masters of business administration with concentration in health care management, but there is no masters of medicine degree that I know of in the United States.
A masters is NOT REQUIRED to get an M.dD, D.D.O, D.O, D.D.S. D.Pharm.or D.V.M in the United States.
My best friend was admitted to a double doctorate program. She did get a masters degree in biophysics/chemistry as probably required for the Ph.D. She decided NOT to get the Ph.D. because P 90% of her time she would be either writing or revising research grants. NOT DOING RESEARCH. She wanted to practice medicine, help people, get married and raise a family. That's exactly what she did. .