Root, 23, who is also a frontline spinner in limited-overs cricket, has been replaced by batsman Ian Bell.
Root was struck by the third ball of his innings on 5 March, but went on to make 107 as England won by 25 runs and claimed the one-day series 2-1.
He flew back to England the following day to undergo a scan.
In Root's absence, England suffered a 27-run defeat by West Indies in the first of three Twenty20 internationals in Barbados on Sunday.
Captain Stuart Broad, who aggravated a long-standing knee problem, will miss the final two matches in the series and may need an injection to get him through the tournament in Bangladesh.
The World Twenty20 begins on 16 March, with England taking on New Zealand in their opening match of the tournament on Saturday, 22 March.
The International Cricket Council approved Root's replacement by Bell, who has not played a Twenty20 international since January 2011.
(BBC Sports)