Rescue workers with sniffer dogs were searching for survivors trapped under twisted metal and concrete as smoke
billowed from the market's ruins.
Emergency Ministry spokesmen put the death toll from Thursday's early morning accident at 49 with 31 injured in hospital. But emergency workers at the scene said the toll could rise further.
"People trapped are calling out. They are knocking. The trouble is: time is going by," Sergei Shoigu, Emergencies Minister, said at the scene, where rescue workers tried to locate survivors as another bitter winter night loomed.
The roof of the market in Bauman district in eastern Moscow caved in at 5.45am (0245 GMT) after an overnight snowfall.
As the death toll edged towards 50, Vladimir Putin, the Russian president, called for a "painstaking investigation" to pin down why the building, built in the 1970s, collapsed.
The collapse came as vendors were setting out their stalls at the start of a national holiday. Many victims were from Azerbaijan and other countries in the Caucasus.
Yuri Luzhkov, the mayor of Moscow, who went to the scene, ruled out the possibility that the disaster was an attack by Chechen separatists to coincide with the armed forces national holiday.
"We can safely say that the collapse of the market's roof is not a terrorist act," he was quoted by RIA agency as saying.
Emergency services sent 50 rescue teams, including firefighters, to extract survivors from the ruins. Survivors were said to be communicating from the debris by mobile phone to help rescue workers locate them.
Yuri Akimov, a senior Emergency Ministry official, said: "Rescuers are hoping that the majority of people trapped can be brought out alive."
The accident evoked memories of a disaster in February 2004, when the roof collapsed at the Transvaal Park swimming pool complex in Moscow, killing 28 people and injuring 200.
Heavy snow has caused roof collapses elsewhere in Europe
this winter, killing 66 people at an exhibition in Katowice,
Poland, and 15 in an ice rink in Bad Reichenhall, Germany.