A video released on Thursday by the group's media arm, Aamaq, purports to show the plane's wreckage in flames and the body of the pilot, strung up on what appears to be a pole.
The Britain-based Syrian Observatory for Human Rights also reported that IS militants shot down a plane near the Deir el-Zour military airport, which is controlled by government forces. The Observatory says the militants later "crucified" the body of the pilot.
IS controls the Deir el-Zour province and parts of the provincial capital with the same name, along with the airport.