There are 4 US Post Offices in Monroe County serving a total of 44,660 residents equating to 11,165 residents per post office. It's estimated that approximately 71,282 packages are handled across the 4 county post offices annually. Monroe County is a county located in the U.S. state of Tennessee. As of the 2010 census, the population was 44,519. Its county seat is Madisonville.