Nottinghamshire's Ball, 25, is to have a scan on a knee injury he suffered in a warm-up game on Monday in St Kitts.
It is South Africa-born 21-year-old Curran's first senior call-up and comes in the middle of his involvement with the England Lions in Sri Lanka.
He is the son of late Zimbabwe all-rounder Kevin Curran, and brother of Surrey and Lions player Sam Curran.
"It's all pretty surreal right now, but I'm giddy, I can't wait to get out there," Curran said.
England opener Alex Hales is also set to join the side after recovering from a hand fracture.
West Indies named their 13-man squad for the three-match series on Tuesday.
The squad features batsman Carlos Brathwaite, who hit four successive sixes in the final over from England's Ben Stokes to win the World Twenty20 last year.
The series begins on Friday in Antigua. The second one-day match also takes place in Antigua - on 5 March - with the third game four days later in Barbados.
West Indies squad: Jason Holder (captain), Devendra Bishoo, Carlos Brathwaite, Kraigg Brathwaite, Jonathan Carter, Shannon Gabriel, Shai Hope (wk), Alzarri Joseph, Evin Lewis, Jason Mohammed, Ashley Nurse, Kieran Powell, Rovman Powell.
England squad: Eoin Morgan (captain), Moeen Ali, Jonny Bairstow (wk), Jake Ball, Sam Billings, Jos Buttler (wk), Tom Curran, Liam Dawson, Steven Finn, Alex Hales, Liam Plunkett, Adil Rashid, Joe Root, Jason Roy, Ben Stokes, Chris Woakes.
All three games are live on BBC Radio Test Match Special, which can be found across BBC Radio 5 live sports extra, BBC Radio 4 long wave and via the BBC Sport website and app from 13:15 GMT each day, with updates on Radio 5 live.
Surrey bowler Tom Curran has been added to England's one-day squad for the West Indies tour as back-up to Jake Ball.