Clips taken by eyewitnesses on Saturday afternoon show a large plume of gray smoke over the city center.
The building ablaze is across the river from Gorky Park, close to the Luzhniki Stadium, which hosted the 1980 Summer Olympics.
Footage shows a barrage of small explosions occurring both in the building and in the sky above it.
A firefighting helicopter has been deployed to the scene to help ground teams quench the fire. A Kamov Ka-32 was filmed scooping water from the Moskva River.
While no official information on the fire was immediately available, videos and reports suggest the building is used as a warehouse to store pyrotechnics.
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