Gonvick is a city in Clearwater County, Minnesota, United States. The population was 263 at the 2020 census. Its peak population was 375 …Gonvick is a city in Clearwater County, Minnesota, United States. The population was 263 at the 2020 census. Its peak population was 375 in 1950. A post office called Gonvick has been in operation since 1900. The city was named for Martin O. Gonvick, a pioneer settler and native of Norway.