An anonymous caller told a law enforcement agency in New York that there were five cases of explosives on the Russian Aeroflot plane, which was carrying 256 people.
The plane made an emergency landing in Iceland and is being investigated, along with luggage and passengers.
The caller warned the explosives would detonate once the plane landed in Moscow.
A spokesman for Keflavik airport in Iceland told the BBC: “The bomb threat was made sometime earlier in the morning and at 05.30 GMT the plane decided to head for Keflavik. The aeroplane landed safely at 06.27.”
According to reports, there is as yet no evidence of a bomb on board the plane.