"The government has accepted the resignation of Adm. Joshi with immediate effect," Defense Ministry spokesman Sitanshu Kar said in a statement.
India's navy has been plagued by accidents in recent years that have raised questions about its safety record.
While at sea for a routine training exercise, the crew on the diesel-powered submarine noticed smoke in the sailors' accommodation. "In the process of controlling the smoke/fire, seven crew members inhaled smoke and felt uneasy," the Defense Ministry said.
A helicopter took the seven to a navy hospital in Mumbai and the navy was trying to locate the two missing crew members, it said.
The submarine was not damaged and was heading back to the Mumbai dockyard, navy Capt. D.K. Sharma said, adding that an inquiry had been ordered into the incident.
The cause of the smoke was not yet known. The submarine did not have any weapons on board since it was on a training and inspection mission, the ministry said.
Last August, another of the navy's Russian-made diesel-powered submarines, the INS Sindhurakshak, caught fire after an explosion and sank at its home port in Mumbai, killing all 18 sailors on board.
In December, the INS Talwar, a Russia-built stealth frigate, slammed into a trawler off India's west coast, sinking the boat and tossing 27 fishermen into the sea. All of the fishermen were rescued.
Another navy frigate ran aground near the Mumbai naval base in January, damaging some equipment. And earlier this month, the INS Airavat, an amphibious warfare vessel, ran aground and its commanding officer was stripped of his duties, the Press Trust of India news agency said.
Sameer Patil, a defense analyst with the Mumbai-based think tank Indian Council on Global Relations, said delays in the acquisition of new submarines to replace an inadequate and aging fleet were taking its toll on the operational capabilities of the Indian navy.
"This is unfortunate because the Indian navy is spearheading India's cooperative engagement with the Indian Ocean region, and policy makers need to pay close attention to our naval fleet," he said.
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