Scotland face Afghanistan in Nagpur on the opening day, while Ireland begin their campaign against Oman in Dharamsala on Wednesday.
The winners of each of the two groups will book a place in the Super 10 phase, beginning on 15 March.
England play Sri Lanka in Mumbai in their first match on 16 March.
In total, 58 matches will be played across eight venues over four weeks, in the sixth edition of the tournament since its inception nine years ago.
England - winners of the competition in 2010 - have been drawn in the same group as defending champions Sri Lanka, 2012 winners West Indies and South Africa, who are second in the International Cricket Council T20 rankings.
Australia are chasing a fourth successive triumph in the women's event, which starts on 15 March and features 10 teams.
England, who won the inaugural Women's World T20 in 2009, are in a group containing India, West Indies, Pakistan and Bangladesh.
The women's final will be played before the men's final in Mumbai on 3 April.
BBC Test Match Special will provide live ball-by-ball commentary on 20 matches, including all England fixtures, plus selected other men's fixtures and England women's games.
The BBC Sport website will show video highlights during all men's matches.
There will be live text commentary on all Scotland and Ireland games in the initial group stage, and on all matches from the Super 10 stage onwards.
And do not forget you can sign up for free wicket, end-of-innings and result alerts on all major nations plus Scotland and Ireland via the BBC Sport app.
It may feature the lower-ranked nations, but there are plenty of reasons to follow this week's action.
Watch the man who invented the 'scoop' shot
Ryan Campbell, 14 years after playing two one-day internationals for Australia, will line up for Hong Kong at the age of 44. He is credited with being the first exponent of the 'scoop' shot, which was made famous by Sri Lanka's Tillakaratne Dilshan and has since become commonplace in the modern game.
Ryan Campbell talks to Stumped about his comeback.
Afghanistan's running could be interesting
While Inzamam-ul-Haq is regarded as one of the greatest batsmen in Pakistan history, he is almost as famous for his dodgy running between the wickets. The man who once tried to fight a spectator during an ODI and also refused to bring his side back on the pitch after they were accused of ball-tampering against England is now Afghanistan coach. Fasten your seat belts.
Oman have their own versions of Gayle and Malinga
Zeeshan Maqsood and Munis Ansari may not be familiar to most people. In left-handed Maqsood, Oman are blessed with a player who "can strike it like Chris Gayle", according to former England all-rounder Derek Pringle, who acted as a consultant during the World T20 qualifier last year. Ansari, meanwhile, bowls with a round-arm action that could have been modelled on Sri Lanka's Lasith Malinga.
There could be controversy
Oman, playing in their first major tournament, have left-arm spinner Aamir Kaleem in their ranks. He was the man who sparked controversy during the qualifiers when he 'Mankaded' Hong Kong batsman Mark Chapman, described as a "cowardly" act by their coach Simon Cook. Kaleem said: "It is not a wrong thing. It is under the rules. Our coaches have told us, 'go ahead and run the batsman out'." Watch this space.
See the 'most beautiful ground in the world'
Still not convinced? How about watching cricket being played at one of the most stunning grounds in the world? Dharamsala in northern India, overlooked by the snow-covered Himalayas, offers guaranteed glorious scenery when it hosts all six Group A games and four further matches throughout the tournament.
It will be tough.
Although Ireland have qualified for the past five World T20s and are regarded by many as the best Associate side not playing Test cricket, they have been drawn in the same group as Bangladesh and Netherlands - both of whom are above them in the ICC rankings.
Bangladesh, an established Test nation, will be familiar with conditions on the sub-continent, while Netherlands knocked Ireland out of the 2014 competition with a remarkable win.
Ireland captain William Porterfield is taking part in his fifth World T20, and their squad also contains the experienced O'Brien brothers, Kevin and Niall, and seamer Boyd Rankin, who won seven ODI and two T20 caps for England before returning to play for his native country.
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Scotland - joint winners of the qualifiers with Netherlands - have never won a game in their two previous World T20s in 2007 and 2009 and must defy expectation if they are to progress from Group B.
Captain Preston Mommsen and seamer Alasdair Evans were named in the team of the tournament for the qualifiers, and coach Grant Bradburn predicts "the floodgates could open now" for his improving side.
Zimbabwe are favourites to progress and join England's Super 10 group, while Afghanistan, featuring the brutal hitting of wicketkeeper-batsman Mohammad Shahzad and led by a thrilling three-pronged pace attack, represent a potent threat.
The World Twenty20 starts in India on Tuesday, with Scotland and Ireland among eight teams aiming to qualify for the main stage of the competition.