Burkettsville was founded after the construction of a railroad line through northern Darke County in 1883. It was one of the last communities to be established in northern Darke or southern Mercer counties.
According to the United States Census Bureau, the village has a total area of 0.18 square miles (0.47 km2), all of it land.
As of the census of 2010, there were 244 people, 96 households, and 76 families residing in the village. The population density was 1,355.6 inhabitants per square mile (523.4 /km2). There were 104 housing units at an average density of 577.8 per square mile (223.1 /km2). The racial makeup of the village was 99.2% White and 0.8%African American. Hispanic or Latino of any race were 0.8% of the population.
There were 96 households of which 30.2% had children under the age of 18 living with them, 68.8% were married couples living together, 5.2% had a female householder with no husband present, 5.2% had a male householder with no wife present, and 20.8% were non-families. 18.8% of all households were made up of individuals and 9.4% had someone living alone who was 65 years of age or older. The average household size was 2.54 and the average family size was 2.88.
The median age in the village was 35.7 years. 24.6% of residents were under the age of 18; 6.5% were between the ages of 18 and 24; 27.5% were from 25 to 44; 24.6% were from 45 to 64; and 16.8% were 65 years of age or older. The gender makeup of the village was 52.9% male and 47.1% female.