It is the first military exercise between the two countries, a senior army official said here. The exercise, christened 'VINBAX' will continue for six days.
India and Vietnam have been exploring ways to strengthen defence cooperation.
Vietnam's Prime Minister Nguyen Xuan Phuc was here last week to participate in the India-ASEAN Commemorative summit and attend the Republic Day celebrations.
The issue of bolstering defence and security cooperation figured prominently during the bilateral talks Prime Minister Narendra Modi had with his Vietnamese counterpart.
India and Vietnam had signed a protocol on defence cooperation in 1994. The partnership was thereafter elevated to strategic level in 2007 and a pact on boosting bilateral defence cooperation was signed in 2009.
The strategic partnership was elevated to a comprehensive strategic partnership in September 2016.