The body was reportedly found Monday in Calhoun County's Albion Township.
Chief Scott Kipp of the Albion Department of Public Safety said 42-year-old Donna Jean Frost was last seen Jan. 14 and reported missing Jan. 20. Police said they think she was killed at her Albion home.
Kipp said the body was in a hole used for burning brush.
Kipp said investigators learned the 47-year-old suspect was in Conover, N.C., and he was arrested Sunday on a warrant for an unrelated charge. He's being returned to Michigan.