The Moscow health authority said the injured included one victim in critical condition, 12 in serious condition and 10 more suffering from lesser injuries, RIA-Novosti news agency reported.
A fire briefly broke out after the disaster, sending up thick clouds of acrid smoke and hampering rescuers' efforts as they searched with sniffer dogs for any survivors.
Emergency workers ordered silence every 15 minutes to listen for sounds of those trapped. At one point they could be seen rushing to dig at 10 different spots.
"Time is running out," Emergency Situations Minister Sergei Shoigu said at the scene.
Rescue workers used metal cutters, hydraulic lifters and pickaxes to clear the ruins of the Basmanny market and knelt down to shout into the holes in search of survivors.
Medical workers tried to help a man trapped under a slab of concrete that left only his hand visible, giving him painkillers through an intravenous drip.
Machines were brought in to blow warm air into the rubble to try to keep victims alive in the near freezing temperatures.
Interfax news agency quoted a senior official with the emergency situations ministry as saying "dozens" of people could still be trapped in the rubble.
President Vladimir Putin said that "rescuers are doing all they can to help the victims." He added: "It is necessary to conduct a detailed inquiry and get objective information about the reasons" for the collapse.
Possible causes
Investigators were considering whether a failure to clear recent heavy snowfall from the roof may have contributed to the cave-in, officials said.
It was the third major building collapse blamed on snow in Europe since last month.
The Moscow market, in service since 1975, was designed by the same architect who drafted the building plans for the Transval aqua park in Moscow where a similar roof collapse two years ago left 28 dead and in which structural flaws were also cited as a focus of investigation.
The architect who designed the market building, Nodar Kancheli, was at the scene. He said "incorrect use" of the building's structure may have been a factor in the disaster.
Media reports said a platform for housing additional market stalls had been built and attached to the roof in violation of building regulations and may have contributed to the collapse.
"The construction of the roof did not plan for this," RIA Novosti news agency quoted Mr Kancheli as saying.
The architect was placed under investigation last year in connection with the Transval aqua park roof collapse on February 14, 2004, but no charges have been brought against him so far.
The Moscow market operates around the clock and was used for wholesale trading overnight when dozens of people work inside, officials said.
The victims were municipal and market workers, most believed to be migrant workers from former Soviet republics.