There were 256 passengers aboard the Airbus A330.
No one was injured, the airline said.
An official with knowledge of the situation but who was not authorized to speak told Newsday it was "a noncredible threat."
The official said the anonymous threat was made to the Port Authority police at about 10 p.m. Wednesday -- about 40 minutes after the flight had departed Kennedy.
Aeroflot Russian International Airlines Flight 103 had been scheduled to depart at 7 p.m. for a regularly scheduled flight to Moscow, but left Kennedy at 9:23 p.m. after being delayed by storms.
The airline said that, while en route, an anonymous caller said a bomb had been placed aboard the aircraft. The flight then diverted to Keflavik International Airport in Reykjavik, Iceland, the airline said.
"During the flight an anonymous call about a bomb aboard an aircraft was received," an Aeroflot customer service representative told Newsday. "So the commander, after receiving this information, he made a decision to land the plane."
But the official source told Newsday all passengers had deplaned in Reykjavik and said the aircraft and baggage had been inspected by security agents there, determining the threat not to be credible.
The airline representative said all passengers were "safe."
The airline could not confirm if passengers on the diverted flight had been placed aboard another aircraft for continuation to Moscow.
The airline said if passengers were delayed a significant amount of time in Reykjavik they would be given hotel rooms and meals.