The explosion occurred at 7:00 p.m. Moscow time (15:00 GMT) on the tenth floor of a 22-storey building, blowing out walls and destroying large parts of the 10th and 11th floors. The blaze engulfed the 10-12th floors.
The blaze has been extinguished.
Speaking at the scene, Moscow Mayor Yury Luzhkov said three people had been killed. They are currently being indentified.
An unidentified emergencies official earlier said that "two corpses, a woman and a teenage boy, were found in an apartment in the tower block as the blaze was being extinguished."
General Viktor Klimkin, deputy head of Moscow's emergencies department, said 16 people, including a 14-year-old boy discovered in one of the apartments, had been rescued.
Experts said it was so far unclear what had caused the explosion.
"Where exactly the explosion went off is yet to be determined. There are no gas ovens in the building," Klimkin said.
Klimkin warned that some floor structures in the building could collapse. He said emergency service workers were now cleaning up the site of the blast and reinforcing parts of the building.
Luzhkov said the explosion was unlikely to turn out to have been a terrorist attack and suggested that welders using faulty equipment could have been to blame.
"Here arises a question the media often asks: are there any signs of a terrorist act here? I believe this is not the case," Luzhkov said.