Saman District () is a former administrative division of Shahrekord County, Chaharmahal and Bakhtiari province, Iran. Its capital was the city of Saman.
In 2013, the district was separated from the county in the establishment of Saman County
At the time of the 2006 National Census, the district's population was 34,457 in 9,273 households. The following census in 2011 counted 35,895 people in 10,772 households.