Breckenridge is a city and county seat of Wilkin County, Minnesota, United States. The population was 3,386 at the 2010 census.Breckenridge's twin city is Wahpeton, North Dakota. It is part of the Wahpeton, ND–MN Micropolitan Statistical Area. The Bois de Sioux River and the Otter Tail River join at Breckenridge and Wahpeton to form the Red River of the North.