Before the Soviet Union occupied Estonia during World War II, around 130 people, mainly Estonian Swedes, lived on the island. The continuous settlement of Swedes on Osmussaar had dated back for centuries. Currently Osmussaar has only two permanent inhabitants and the island is a nature reserve.
The island's Swedish name Odensholm (or Odinsholm) derives from the Vikings' chief god, Odin, who, according to a legend, is buried on the island. The origin of the Estonian name Osmussaar is not clear.