Medicine Park is a town in Comanche County, Oklahoma, United States, situated in the Wichita Mountains near the entrance to the 60,000-acre Wichita Mountain Wildlife Refuge. Medicine Park has a long history as a vintage cobblestone resort town. Medicine Park is located near the city of Lawton and Fort Sill. It is an exurb, part of the Lawton Metropolitan St…Medicine Park is a town in Comanche County, Oklahoma, United States, situated in the Wichita Mountains near the entrance to the 60,000-acre Wichita Mountain Wildlife Refuge. Medicine Park has a long history as a vintage cobblestone resort town. Medicine Park is located near the city of Lawton and Fort Sill. It is an exurb, part of the Lawton Metropolitan Statistical Area. Many of the original structures are constructed of naturally formed cobblestones—these red granite cobblestones are unique to the Wichita Mountains. The population was 382 at the 2010 census.