In January, Plunkett replaced Finn in the limited overs squads against South Africa after suffering a side strain in the third Test match in Johannesburg.
At that time Finn was expected to recover in time for the ICC World T20 but he picked up a calf injury while recovering from his side strain.
Finn took to twitter to voice his disappointment at missing out on the ICC World T20 and wished the England squad the best for the tournament.
"Really disappointed to have picked up another injury on my road to recovery,” wrote Finn on twitter.
"Gutted doesn't describe it.
“Good luck to the guys out there!"
England will play two warm-up matches in Mumbai on 12th and 14th March before beginning their campaign in the ICC World T20 with a game against West Indies on 16th March.
England ICC World T20 squad
Eoin Morgan (capt), Moeen Ali, Sam Billings, Jos Buttler, Liam Dawson, Alex Hales, Chris Jordan, Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, Ben Stokes, Reece Topley, James Vince, David Willey
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