The 26-year-old Middlesex quick was down to lead England’s attack at next month’s global tournament in India despite missing the white ball section of the recent tour of South Africa with a side strain.
But Finn has suffered a fresh injury blow and his place in England’s 15-man squad will now be taken by Yorkshire fast bowler Liam Plunkett.
England leave for India on March 8 and will face Sri Lanka, South Africa, West Indies and a qualifier in the group stages of the tournament.
The only major International Cricket Council limited-overs trophy England have ever won was the 2010 World Twenty20 in the Caribbean.
Last week they suffered a nine-wicket thrashing by South Africa as the Proteas took a two-match Twenty20 series 2-0 with a crushing win in Johannesburg.
