The plane was operated by the small Russian airline Kogalymavia, based in western Siberia.
Russian authorities say it was carrying 217 passengers, 17 of them children, and seven crew. Most were tourists.
A centre to help relatives of the passengers has been set up at Pulkovo airport, Tass news agency quoted St Peterburg city officials as saying.
Sudden altitude loss
Initially there were conflicting reports about the fate of the plane, some suggesting it had disappeared over Cyprus.
But the office of Egyptian Prime Minister Sharif Ismail confirmed in a statement that a "Russian civilian plane... crashed in the central Sinai".
It added that Mr Ismail had formed a crisis committee to deal with the crash.
Media reports say at least 50 ambulances have been sent to the scene.
The Russian aviation authority Rosaviatsiya said in a statement that flight 7K 9268 left Sharm el-Sheikh at 06:51 Moscow time (03:51 GMT) and had been due into St Petersburg's Pulkovo airport at 12:10.
The authority added that the aircraft failed to make scheduled contact with Cyprus air traffic control 23 minutes after take-off and disappeared from the radar.
Egypt's civilian aviation ministry said the plane had been at an altitude of 9,500m (31,000ft) when it disappeared.
Live flight tracking service Flight Radar 24's Mikail Robertson confirmed the altitude.
He told the BBC that the plane started to drop very fast, losing 1,500m in one minute before coverage was lost.
The BBC's Orla Guerin in Cairo says it is likely there will be speculation about militant involvement in the incident - Sinai has an active militant network, with local Jihadis who have allied themselves to so-called Islamic State.
But the aircraft's altitude suggests that it could not have been struck from the ground, she adds.
An official investigating the crash quoted by al-Ahram newspaper said it was caused by a "technical failure".
The pilot had detected a problem and requested an emergency landing at the nearest airport, Ayman al-Mokadem said.
Local weather observations in the vicinity of the rescue scene suggest relatively benign conditions.