The bomb went off at about 10.30am (0630GMT) in the Cherkizovsky market in northeastern Moscow on Monday.
Officials said that although the explosion was almost certainly caused by a bomb, the attack was likely part of a criminal or commercial dispute rather than a political act.
Yury Semin, a Moscow prosecutor, told journalists at a briefing near the explosion site: "The most likely hypothesis is that the explosion was motivated by commercial competition or a dispute between criminal groups."
Russia's Interfax news agency reported that two suspects had been detained.
Interfax cited unidentified investigators as saying both suspects had been seen leaving a bag near one of the market's pavilions shortly before the explosion.
Vladimir Resin, Moscow's deputy mayor, said a homemade bomb caused the blast.
The explosion caused a 200 square metre section of the market to collapse, Yulia Stadnikova, a spokeswomen from the ministry for emergency situations said.
She said at least two of those killed were children. An Aljazeera reporter at the scene had said that four children had been killed.
City prosecutor Yuri Syomin told reporters at the scene that 41 people had been hospitalized.
The market is popular with immigrants from East Asia.
Business violence in the Russian capital is less frequent than in the post-Soviet 1990s, but guns and bombs are still sometimes used to settle commercial disputes while armed criminal gangs are also active.