The cause of the blast is under investigation, but Moscow Deputy Mayor Vladimir Resin was quoted by Interfax news agency as saying it appeared to have "intentional" and caused by a homemade bomb.
That contradicted earlier comments from other officials and witnesses quoted by Russian media who said the blast was an accident caused by the explosion of a gas container.
The area around the market was chaotic, with alarms ringing, rescue vehicles trying to get close to the site and panicked traders massing in the surrounding streets.
The blast occurred at the Eurasia market in eastern Moscow, a two-story shopping pavilion noted for its many traders of Chinese and Vietnamese origin.
Officials said about 200 square meters of stalls had been destroyed by the blast, along with about 100 square meters of the market's roof.
Access to the site for police and rescuers was hampered in the immediate aftermath of the explosion by panicked merchants blocking streets as they tried to flee with their wares, witnesses said.
Spokesmen for the local and federal branches of the emergency situations ministry said eight people had been confirmed dead, while other officials put the death toll at 10.
At least two of the dead were children, the ministry said.
Figures on the number of people hurt in the explosion are also unclear, ranging from between 13 to 30.