The 345-foot ship is the 200th vessel built by Goa Shipyards on India's west coast, the Times of India reported.
The 2,300-ton Sumedha is of the largest offshore patrol vessel class of the Indian navy and the largest ship constructed by Goa Shipyards, The Times reported.
The first ship, the Saryu, was handed over to the navy in December 2012 and the second ship, Sunayna, was handed over in September last year.
Anand Kulkarni, commanding officer-designate of the Sumedha, accepted the vessel on behalf of the navy during a ceremony at the shipyard, the Times reported.
Saryu-class vessels have a crew of 108, two SEMT Pielstick diesel engines and can reach more than 25 knots with a range of 6,000 nautical miles.
The ships have a 76mm Ottomelara gun, two 30mm close-in guns and six chaff launchers for self-protection.
Saryu vessels also have a helicopter landing deck for light helicopters and have two rigid inflatable fast motor boats.
The handover comes as the navy hopes to replace its aging fleet of 12 Pondicherry and Karwar class minesweepers.
Defense analysts Janes Defense Weekly reported in October India had signed a $1.2 billion contract with South Korean shipyard Kangnam for eight minesweepers.
The Hindu newspaper reported in 2011 the proposed deal Kangnam Corp. calls for building two of the vessels at the shipyard in Busan, South Korea.
The other six will be manufactured by Goa Shipyards after a transfer-of-technology agreement.
India's 200-foot long Pondicherry-class ships were built for the Indian navy by the Soviet Union from 1978 to 1988 and are modified versions of the Russian Natya-class minesweepers.
Later Pondicherry-class vessels often are referred to as Karwar-class ships because of upgrades and the addition of surface-to-air missiles.
The Indian government also is looking to build four landing platform docks, but sidelined the Cochin Shipyard in December when it announced the list of private firms that could be building the vessels.
The Times of India quoted sources as saying the navy had sent bid documents to three private shipyards: ABG Shipyard, Larsen & Toubro and Pipavav Defense and Offshore Engineering.
The government already has chosen state-run Hindustan Shipyard to build two of the landing platform docks and the winning company among the three private shipyards will build the remaining two.
"We understand that some rethinking is going on with the [navy] exploring the possibilities of including CSL in this deal," a senior Cochin Shipyard official told the Times.