The victims are thought to have been conducting a search inside the building when its roof collapsed.
Earlier, they had managed to lead to safety more than 100 workers at the warehouse where plastic materials and gas canisters were stored.
A search is continuing at the site in Golyanovo, north-east Moscow.
There are suspicions that the fire was caused by a violation of safety regulations.
"The corpses of eight colleagues have been found in the main area where the search was located," the emergency services ministry said in a statement.
"Until the end there was hope that they would be alive. But due to the intense fire, the high temperatures and the thick smoke the firefighters were unable to get out."
Firefighters prevented the explosion of 30 cylinders of household gas in the warehouse, as well as discharging 67kg (148lb) of ammonium from a compressor facility, the emergency ministry also said, quoted by Tass news agency.
The fire - which reportedly engulfed an area of 4,000 sq m (43,000 sq feet) - was finally extinguished at 07:44 local time (04:44 GMT).
There are suspicions that radiators had been left on, overwhelming the building's electricity circuit.
This is the latest deadly inferno to hit the Russian capital, where safety standards are often low.
In January, 12 people including three children died in a huge fire at a textile factory in the east of the city.
Russian rescuers in Moscow have found the bodies of eight firefighters in the remains of a large warehouse that was engulfed by fire late on Thursday.