Monticello (/ˌmɒntɪˈsɛloʊ/ MONT-i-SEL-oh) is a city in Wright County, Minnesota, United States. The population was 12,759 at the 2010 census.Monticello is located on the Mississippi River at the northern edge of Wright County. Each winter, hundreds of trumpeter swans nest near Mississippi Drive Park in Monticello, as the Mississippi River is heated from warm water discharged by the Monticello Nuclear Generating Plant.