There are 5 US Post Offices in Monroe County serving a total of 5,548 residents equating to 1,110 residents per post office. It's estimated that approximately 8,855 packages are handled across the 5 county post offices annually. Monroe County is a county located in the northeastern portion of the U.S. state of Missouri. As of the 2010 census, the population was 8,840. Its county seat is Paris.