One of the cleanest strikers of the ball and more than a handy left-arm spinner, Singh, 32, was instrumental in India's triumph in the inaugural World Twenty20 in 2007 where he hit England paceman Stuart Broad for six sixes in an over.
Though he could not cement his place in the test squad, Singh, 32, was also the architect of India's 50-over World Cup 2011 victory at home where his all-round exploits earned him the player of the tournament award.
Singh was not part of the Indian 50-over squad in New Zealand which lost the five-match series 4-0.
Stuart Binny, son of former India all-rounder Roger, was also named in the squad to be led by Mahendra Singh Dhoni who would be seeking his third world title in Bangladesh.
Off-spinner Ravichandran Ashwin and all-rounder Ravindra Jadeja are expected to share the spin workload even though the selectors included a third spinner in leggie Amit Mishra.
India begin their World Twenty20 campaign against 2009 champions Pakistan in Dhaka on March 21.
Squad: Mahendra Singh Dhoni (captain), Shikhar Dhawan, Rohit Sharma, Virat Kohli, Suresh Raina, Yuvraj Singh, Ajinkya Rahane, Ravindra Jadeja, Ravichandran Ashwin, Bhuvneshwar Kumar, Mohammed Shami, Stuart Binny, Amit Mishra, Mohit Sharma, Varun Aaron.