The Central District of Baft County () is in Kerman province, Iran. Its capital is the city of Baft.
After the 2006 National Census, Dehsard Rural District was separated from the district in the establishment of Arzuiyeh County, and Dashtab and Khabar Rural Districts were separated from it in the formation of Khabar District.
At the time of the 2006 census, the district's population was 68,270 in 16,394 households. The following census in 2011 counted 59,112 people in 16,356 households. The 2016 census measured the population of the district as 67,520 inhabitants in 21,051 households.