As of 2000 the median income for a household in the city was $36,922, and the median income for a family was $47,361. Males had a median income of $32,050 versus $22,112 for females. The per capita income for the city was $21,657. About 2.4% of families and 5.4% of the population were below the poverty line, including 4.3% of those under age 18 and 8.1% of those age 65 or over.
As of the census of 2010, there were 10,827 people, 4,810 households, and 2,781 families residing in the city. The population density was 2,241.6 inhabitants per square mile (865.5/km2). There were 5,101 housing units at an average density of 1,056.1 per square mile (407.8/km2). The racial makeup of the city was 94.8% White, 0.6% African American, 0.2% Native American, 0.7% Asian, 2.6% from other races, and 1.1% from two or more races. Hispanic or Latino of any race were 4.9% of the population.
There were 4,810 households of which 27.4% had children under the age of 18 living with them, 42.8% were married couples living together, 10.7% had a female householder with no husband present, 4.3% had a male householder with no wife present, and 42.2% were non-families. 36.4% of all households were made up of individuals and 16.9% had someone living alone who was 65 years of age or older. The average household size was 2.22 and the average family size was 2.87.
The median age in the city was 41.1 years. 22.5% of residents were under the age of 18; 8% were between the ages of 18 and 24; 24% were from 25 to 44; 26.8% were from 45 to 64; and 18.8% were 65 years of age or older. The gender makeup of the city was 47.9% male and 52.1% female.
The Monroe School District is the largest school district in Green County, serving around 2,700 pupils, and having an open enrollment procedure. The school district maintains Monroe High School, home of the Cheesemakers in the Badger Conference, Monroe Middle School, Abraham Lincoln Accelerated Learning Academy, Parkside Elementary School, and Northside Elementary School. The district also has an alternative high school and middle school, as well as a virtual school. St. Victor Catholic elementary school also serves the community. Monroe has a campus of Blackhawk Technical College, the community's sole institution of post-secondary education.
Monroe has a number of large parks. The largest include Twining Park, where the city's Swiss bandshell is located; Recreation Park, home to the city swimming pool; and Honey Creek Park, the location of a skate park. The city is the eastern starting point for the Cheese Country Trail, a 47-mile multi-purpose recreational path, and the Badger State Trail, a bicycle and pedestrian-only trail in summer and an ATV/snowmobile trail in winter. The "Cheese Trail" extends from Mineral Point to Monroe, while the Badger State Trail runs from the state line to Madison and connects to the Jane Addams Trail in Illinois. Both are former railway corridors. Monroe is also home to Stateline Ice and Community Expo (S.L.I.C.E.), the only indoor ice-rink in Green County.