"The crew was able to move the aircraft to the side on time and save the lives of the passengers," the source said, adding that it was unclear whether the attackers knew that the plane was Russian.
The plane was returning from a resort in Egypt, a popular destination for Russian tourists.
The federal air transport agency Rosaviation issued a statement later Monday, saying the crew of a charter plane flying from the Egyptian resort of Sharm-el-Sheikh to the Russian city of Kazan had detected "signs of combat actions" when it was flying over Syria.
The crew of the A-320 plane, which belongs to NordWind Airlines, believed that those actions threatened the aircraft's safety, said the agency, adding that the plane landed in Kazan on time.