The incident took place when the pressure of the hydraulic tank of the Arihant class submarine was being tested and the tank's lid fell on the workers of at Building-5 of the shipbuilding cente, said Defence Research Development Organisation (DRDO) chief Avinash Chander.
He said one worker "unfortunately lost his life" in the incident.
Police sources said 24-year-old Amar was killed on the spot while Amzad Khan and Vishnu were seriously injured and admitted to a private hospital in the city.
The under-construction nuclear submarine was a follow-up of the Navy's warship INS Arihant.
Chander said an inquiry has been ordered into the incident and maintained there was no setback to the programme for development of Arihant class submarines.
Saturday's incident came a day after leakage of a deadly gas in an under-construction warship in Mumbai's Mazagon dock claimed the life of a Navy Commander.
This is the 12th incident involving naval assets in service in the recent past or which are expected to join the Navy in near future.
Around 10 days ago, warship INS Sindhuratna had suffered a mishap under water when smoke and fire killed two officers and the incident led to the exit of former Navy Chief Admiral DK Joshi who resigned taking moral responsibility over the spate of incidents.
The biggest mishap had occurred when the INS Sindhurakshak sank in Mumbai harbour, killing all the 18 personnel on board on August 14.
Last month, INS Airavat, an amphibious warfare vessel, had run aground after which the commanding officer was stripped of his command duties.
After the sinking of the INS Sindhurakshak, one of the mishaps involved INS Betwa which was damaged apparently after hitting an underwater object.
India's leading minesweeper INS Konkan, that was undergoing repairs in Visakhapatnam, had caught fire and suffered major damage to its interiors. The Pondicherry-class minesweeper was getting a refit at a dry dock when the incident occurred.
Under the Arihant class submarine development programme, India is building around three submarines which have not yet been named so far.
The first vessel of the class INS Arihant is expected to be launched for sea trials within a month or two and these are expected to be completed within this year.
Recently, Navy officials had said that after the trials of INS Arihant are completed, it would be ready for induction into operational service.
The ATV project is directly under the DRDO and the Navy plays a significant role it it.