The batsman, whose century in Wednesday's ODI in Antigua was critical in England winning the match and the series, could also miss the ICC World T20, which begins on 16 March in Bangladesh.
Root is flying home to England to see a specialist and get further advice.
The 23-year-old sustained the injury during his 107-run innings, but he played on and said later that, "It's a little sore but it should be all right."
England are due to play three T20 matches against the West Indies before they head to the subcontinent to play in the tournament, which they won in 2010.
Their first World T20 match is against New Zealand on March 22 followed by games against Sri Lanka, South Africa and one of the minor nations.
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