The 21-year-old, who has been part of the England Lions squad in Sri Lanka, will fly to the Caribbean as cover for Jake Ball who injured his knee in a warm-up match on Monday.
England play the first of three ODIs in Antigua on Friday.
"It's all pretty surreal right now," Curran said in a statement from the England and Wales Cricket Board.
"I can't wait to get out there."
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Surrey bowler Curran, born in Cape Town, qualified to play for England last year.
He shot to prominence in 2015 when he and younger brother Sam took all 10 wickets between them in an innings in a County Championship game against Northamptonshire.
(Reporting by Martyn Herman; Editing by Alison Williams)
