The spin-bowler, who is yet to have represented his country in any format, has spent his entire county career with Hampshire.
At T20 level for Hants, the 25-year-old has taken 39 wickets from 73 matches at an average of 29.87.
Meanwhile, with the bat Dawson has scored 495 runs from the same number of outings, with a highest score of 45 not out.
There are no further surprises within the squad, which will be skippered by Eoin Morgan.
England get their campaign in India underway with a group clash against the West Indies on Wednesday, March 16.
England's T20 squad: Eoin Morgan (Middlesex), Moeen Ali (Worcestershire), Sam Billings (Kent), Jos Buttler (Lancashire), Liam Dawson (Hampshire), Steven Finn (Middlesex), Alex Hales (Nottinghamshire), Chris Jordan (Sussex), Adil Rashid (Yorkshire), Joe Root (Yorkshire), Jason Roy (Surrey), Ben Stokes (Durham), Reece Topley (Hampshire), James Vince (Hampshire)