Re-entry was over the Pacific, it said, and only a few fragments were expected to hit the sea.
The unmanned cargo ship was launched from Kazakhstan on 28 April, but control was lost soon afterwards.
Russian space agency Roscosmos said: “The Progress M-27M spacecraft ceased to exist at 05:04 Moscow time (02:04 GMT) on 8 May 2015. It entered the atmosphere… over the central part of the Pacific Ocean.”
Progress was to deliver food, water, fuel, oxygen and clothing to the crew of six people on the ISS, which orbits about 420km (250 miles) above Earth.
But after a communications failure, it began spiralling out of control.
The capsules were designed to burn up in the atmosphere after delivering their cargo.
A special commission has been set up in Russia to investigate why Progress was lost.
In 2011, one of its predecessors was destroyed when it crashed soon after take-off in Siberia.
Even after Progress’ loss, the astronauts have enough supplies to keep them going until the next expected delivery on 19 June.
A Roscosmos spokesman told Reuters that the loss was valued at 2.59 billion roubles ($50.7m; £32.9m).