The MiG-21 came down on Thursday night in the desert of western Rajasthan state near the city of Barmer, the defence ministry said.
The crash was the sixth MiG-21 aircraft to have gone down since January last year, with five pilots killed.
The Indian Air Force (IAF) said the training aircraft "met with an accident" and said an investigation was ordered to determine the cause of the crash.
"IAF deeply regrets the loss of lives and stands firmly with the bereaved families," the air force tweeted.
Local media footage showed flaming wreckage spread over a large area.
Defence Minister Rajnath Singh said he was "deeply anguished" by the loss of the two pilots in the crash.
"Their service to the nation will never be forgotten," Singh said on Twitter.
MiG-21 jets first entered Indian service in the 1960s and for decades served as the backbone of the country's air force.
Numerous crashes in the past few decades, however, have led to the planes being dubbed "flying coffins" because of their poor safety record.
India is investing billions of dollars in modernising its air force, an initiative motivated by its decades-old rivalry with Pakistan and increased tensions with China.
Its military has bought dozens of French Rafale fighter jets, with deliveries starting in 2020.
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