Finn, 26, was forced out of England's tour of South Africa in January with a side strain, but has withdrawn from the upcoming tournament in India with a left calf problem.
Plunkett, 30, was in the England party for the T20 leg of the South Africa tour, but did not play in either game.
England's first World T20 game is against West Indies on 16 March.
Pace bowler Steven Finn has been ruled out of England's ICC World Twenty20 squad and replaced by Liam Plunkett.