Fort Washakie is a census-designated place in Fremont County, Wyoming, United States, within the Wind River Indian Reservation and along U.S. Route 287. The population was 1,759 at the 2010 census. The headquarters for the Eastern Shoshone Tribe is located in Fort Washakie, as well as the Bureau of Indian Affairs agency for the Wind River Indiā¦Fort Washakie is a census-designated place in Fremont County, Wyoming, United States, within the Wind River Indian Reservation and along U.S. Route 287. The population was 1,759 at the 2010 census. The headquarters for the Eastern Shoshone Tribe is located in Fort Washakie, as well as the Bureau of Indian Affairs agency for the Wind River Indian Reservation.