It was first settled in 1854. On February 26, 1869, the settlement was granted a post office with the name of Skinner. On November 19, 1877, the Skinner Post Office was renamed Auburn.
As of the census of 2010, there were 2,087 people, 916 households, and 551 families living in the city. The population density was. There were 960 housing units at an average density of. The racial makeup of the city was 97.5% White, 0.3% African American, 0.8% Native American, 0.5% Asian, 0.1% Pacific Islander, 0.3% from other races, and 0.5% from two or more races. Hispanic or Latino of any race were 2.0% of the population. There were 916 households, of which 28.2% had children under the age of 18 living with them, 43.2% were married couplesliving together, 12.7% had a female householder with no husband present, 4.3% had a male householder with no wife present, and 39.8% were non-families. 34.5% of all households were made up of individuals, and 13.5% had someone living alone who was 65 years of age or older. The average household size was 2.24 and the average family size was 2.87. The median age in the city was 40.9 years. 22% of residents were under the age of 18; 9.1% were between the ages of 18 and 24; 24.3% were from 25 to 44; 27.1% were from 45 to 64; and 17.6% were 65 years of age or older. The gender makeup of the city was 47.6% male and 52.4% female.
2000 census
As of the census of 2000, there were 2,011 people, 842 households, and 553 families living in the city. The population density was 1,971.6 per square mile. There were 867 housing units at an average density of 850.0 per square mile. The racial makeup of the city was 97.51% White, 0.35% African American, 0.55% Native American, 0.30% Asian, 0.35% from other races, and 0.94% from two or more races. Hispanic or Latino of any race were 2.39% of the population. There were 842 households, out of which 32.5% had children under the age of 18 living with them, 50.4% were married couples living together, 13.2% had a female householder with no husband present, and 34.3% were non-families. 29.1% of all households were made up of individuals, and 9.6% had someone living alone who was 65 years of age or older. The average household size was 2.37 and the average family size was 2.97. In the city, the population was spread out, with 25.6% under the age of 18, 8.4% from 18 to 24, 29.8% from 25 to 44, 22.6% from 45 to 64, and 13.6% who were 65 years of age or older. The median age was 37 years. For every 100 females, there were 92.4 males. For every 100 females age 18 and over, there were 86.1 males. The median income for a household in the city was $42,014, and the median income for a family was $51,442. Males had a median income of $41,927 versus $25,720 for females. The per capita income for the city was $20,941. About 5.1% of families and 6.4% of the population were below the poverty line, including 9.5% of those under age 18 and 11.6% of those age 65 or over.
