Elgin is a city in Wabasha County, Minnesota, United States on Minnesota State Highway 42. The population was 1,089 at the 2010 census. Its …Elgin is a city in Wabasha County, Minnesota, United States on Minnesota State Highway 42. The population was 1,089 at the 2010 census. Its annual festival is Elgin Cheese Days. Elgin was laid out in 1878 when the railroad was extended to that point. The city was named after Elgin, in Scotland.