The Corvette for Vietnam is the first time India has given a warship to a Chinese neighbour.
An active-duty missile corvette of the Indian Navy is on its way to Vietnam as a gift, the first warship given by India to any country.
The domestically built corvette INS Kirpan left India's east coast on Wednesday, the navy said.
India and Vietnam have strengthened their ties in recent years, with a special focus on defence, as both countries are concerned over an increasingly assertive China.
India has given smaller boats and military equipment to countries like Maldives and Mauritius in the past and a submarine to Myanmar.
But the Corvette for Vietnam is the first time India has given a warship to a Chinese neighbour with a coast on the South China Sea, where several countries have overlapping territorial claims.
China has for years claimed sovereignty over the entire South China Sea, and has been sensitive to the presence of other militaries in the region.
The Indian Navy said in a statement the transfer of the Kirpan "reflects India's commitment to assist its like-minded partners in enhancing their capacity and capability".
"This is the maiden occasion of gifting a fully operational corvette by India to any Friendly Foreign Country."
The gift was announced when Vietnam's Defence Minister Gen Phan Van Giang visited India earlier this month.
The warship was commissioned into the Indian Navy in 1991 and has been designed and produced within the country.
It is fitted with medium-range and close-range guns, chaff launchers and surface-to-surface missiles, the navy said. It did not mention if the transfer included missiles.
Chinese Defence Minister Li Shangfu said on Tuesday that Beijing is willing to work with Hanoi to strengthen high-level communication and cooperation after he met his Vietnamese counterpart.
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