The session will form one of the eight episodes of Emmy-winning TV series "Years of Living Dangerously".
Letterman, 68, will return to TV with show's second season after retiring from "Late Show" in May, said The Hollywood Reporter.
The series centres on the issue of climate change.
Producers Joel Bach and David Gelber explained about how Letterman came on board, saying they decided to reach out to him after seeing his passion for the issue when he interviewed scientists on the "Late Show".
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"He's never been to India, and he's really excited to go," Gelber said of Letterman.
"Dave will be a terrific correspondent for us. We're very comfortable having him with the Prime Minister of India - I'm not sure there are that many people we'd be comfortable setting up in that kind of role. He's a wonderful interviewer."
Other guests set for season two include Ty Burrell, James Cameron, Don Cheadle, Arnold Schwarzenegger, Olivia Munn, Ian Somerhalder and Cecily Strong.
Burrell's episode will focus on electric cars, while Schwarzenegger will be visiting China.