Munroe Falls is a city in east-central Summit County, Ohio, United States, along the Cuyahoga River. The population was 5,044 at the 2020 ce…Munroe Falls is a city in east-central Summit County, Ohio, United States, along the Cuyahoga River. The population was 5,044 at the 2020 census. It is a suburb of Akron and is part of the Akron metropolitan area.