In a statement to Russian news agencies, the defence ministry said the MiG-29K fighter crashed due to a "technical fault" a few kilometres from the carrier.
The pilot ejected and was recovered and taken aboard the ship. "The pilot's health is in no danger. The pilot is ready to carry out missions," the ministry said, quoted by Interfax news agency.
The defence ministry did not say when the incident occurred, but said the plane was taking part in training flights. It stressed that flights were still going ahead from the aircraft carrier despite the accident.
The Admiral Kuznetsov aircraft carrier arrived in the eastern Mediterranean off the Syrian coast as part of a flotilla of ships sent to reinforce Russia's military in the area, its commander confirmed on state television.
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The ship's commander Sergei Artamonov said in an interview broadcast Saturday on Rossiya-1 television that planes had been taking off from the ship's deck "practically every day for the last four days" to survey the area.
The flotilla including the Admiral Kuznetsov has sparked concern from NATO that it will be used to take part in air strikes on Syria.