The passenger jet crashed in Egypt's Sinai peninsula, where wreckage has been found, according to Russia's RIA news agency.
There was no immediate word on whether anyone survived the crash or what may have caused it, although poor weather conditions may have played a part.
As many as 17 children may have been on the plane.
The Sinai is a sparsely populated and rugged desert region sandwiched between the southern Mediterranean Sea and the Red Sea.
Most of the people on board were thought to be Russian tourists. Sharm el-Sheikh is a resort city known for its sandy beaches. It is a popular destination for divers.
Prime Minister Ismail confirmed the Airbus-321 jet crashed after earlier conflicting reports suggested the plane may have simply lost contact with air traffic controllers somewhere over Turkish airspace.
The plane, operated by Kogalymavia Airlines, was traveling from Sharm el-Sheikh to St Petersburg. Kogalymavia also sometimes goes by the name Metrojet.
Alternative Airlines, an online travel agency, describes Kogalymavia/Metrojet as "an airline based in the oil producing town of Kogalym in the Urals region of Russia."
Flight Radar 24, a flight tracking service, said the plane was descending at 6,000 feet per minute when it disappeared from air traffic controllers' radar screens.
