Root suffered the injury during England's One-day series clincher in the West Indies and the ICC said in a statement that it has approved Bell as his replacement ahead of the tournament, which begins on March 16.
Root scored his first international limited-overs century during the three-match series in the West Indies, which England won 2-1.
He played all three games and was injured in the series decider after being struck on the thumb by a Ravi Rampaul delivery.
Test veteran Bell has represented England in seven T20 matches, in which he scored 175 runs, and will join up with the squad ahead of their first match of the tournament against New Zealand on March 22.
The news comes as another injury blow for England after captain Stuart Broad was ruled out for the remainder of their T20 series against the West Indies, which began with a 27-run defeat in Barbados on Sunday.
Broad is suffering from an ongoing knee injury, but hopes to be fit for the World T20 opener.
West Indies are the defending World T20 champions and the three-game series against England, who won the title in 2010, is a precursor for the fifth edition of the tournament.
The series resumes on Tuesday, with the West Indies leading 1-0.
Image: Joe Root
Photograph: Paul Gilham/Getty Images
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