Navy chiefs earlier warned the families of 18 sailors on board the submerged vessel to "prepare for the worst" after the two near-simultaneous explosions.
Mr Antony offered "heartfelt condolences" to relatives of the dead.
Sabotage not ruled out
Indian emergency services say it is not clear what caused the blasts and "sabotage has not been ruled out".
"A board of inquiry will cover the entire spectrum of the incident, we cannot rule out sabotage at this stage but all the indicators at this point do not support that theory," navy chief Admiral DK Joshi said.
"Divers have opened the first hatch of the [submerged] submarine and are in the process of going down now. A detailed examination can only be carried out after the water is pumped out and the boat has come back to the surface."
Dramatic images on Indian television showed a large fireball illuminating the sky. Smoke from the blaze could be seen in many parts of the city.
The INS Sindhurakshak, which is powered by diesel and electricity, is one of the 10 Kilo-class submarines bought from Russia between 1986 and 2000. It is equipped with Russian Club-S cruise missile systems.