Denmark is an unincorporated community and census-designated place in northeastern Lee County, Iowa, United States. It lies along Iowa Highway 16, north of the city of Fort Madison, the county seat of Lee County. Its elevation is 722 feet above sea level. Although Denmark is unincorporated, it has a post office with the ZIP code of 52624, that opened on April 7, 1846. The town also has a branch of Farmers Savings Bank that opened in 1935.