That depends entirely on which Monroe County you are requesting information about. There are seventeen Monroe Counties in various states across the US. According to census.gov, the 2007 estimated total population of each of these Monroe Counties and which state they are located in are listed alphabetically as follows:
# Monroe County, Alabama: 22,764 # Monroe County, Arkansas: 8,712 # Monroe County, Florida: 73,223 # Monroe County, Georgia: 25,145 # Monroe County, Illinois: 32,372 # Monroe County, Indiana: 128,643 # Monroe County, Iowa: 7,586 # Monroe County, Kentucky: 11,663# Monroe County, Michigan: 153,608 # Monroe County, Mississippi: 37,078 # Monroe County, Missouri: 9,205# Monroe County, New York: 729,681 # Monroe County, Ohio: 14,258 # Monroe County, Pennsylvania: 164,722 # Monroe County, Tennessee: 44,848 # Monroe County, West Virginia: 13,537 # Monroe County, Wisconsin: 43,112