Alexander Gavrilov, deputy chief of the Moscow emergency services, said rescuers had recovered seven bodies and were working to extract 12 more from two wrecked train cars.
Moscow's transit system has been previously targeted by terrorists but Russian officials dismissed terrorism as a possible cause.
Injured passengers were carried out on stretchers, bloodied and bandaged, and helicopters ferried the most seriously hurt people to hospital.
Passengers looked stunned or were crying after being helped to the surface by emergency services.
Investigators said that a power surge had caused the train to stall and several cars to come off the rails.