Wood Lake is a city in Yellow Medicine County, Minnesota, United States. The population was 439 at the 2010 census. Wood Lake was laid ou…Wood Lake is a city in Yellow Medicine County, Minnesota, United States. The population was 439 at the 2010 census. Wood Lake was laid out in 1884, when the railroad was extended to that point. The town took its name from nearby Wood Lake. Wood Lake was incorporated in 1891.