The 26-year-old could only manage two overs during England's one-day international win over India in Kolkata last month before a problem with his left shoulder saw him leave the field and forced him out of the subsequent Twenty20 series.
A left-arm fast-medium bowler and hard-hitting batsman, Willey -- the son of former England batsman and international umpire Peter Willey -- has appeared in 25 ODIs and 12 Twenty20 internationals.
His place in England's 14-man squad for next month's three ODIs in the Caribbean has been taken by Middlesex fast bowler Steven Finn.
"He has suffered a partial tear of a tendon and will be out of action until April."
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The injury has come at a particularly bad time for Willey, looking to secure his place in the one-day international side ahead of the 50-over Champions Trophy tournament in England and Wales in June.
England, who will be captained by Eoin Morgan, a longstanding team-mate of Finn at Middlesex, are due to fly to the Caribbean a week on Wednesday, with star batsman Joe Root appointed Test skipper since the squad was first announced.
They will play two warm-up matches before the first ODI in Antigua on March 3, with Finn vying for a place in England's seam-bowling line-up with Jake Ball, Liam Plunkett and Chris Woakes.
Revised England ODI squad for West Indies tour
Fixtures:
Feb 25: Warm-up match, (50 overs): WICB President's XI v England XI, Warner Park, St. Kitts & Nevis (1330 GMT)
Feb 27: Warm-up match (50 overs), WICB President's XI v England XI, Warner Park, St. Kitts & Nevis (1330 GMT)
Mar 03: 1ST ODI, WEST INDIES v ENGLAND, Sir Vivian Richards Cricket Ground, Antigua (1330 GMT)
Mar 09: 3RD ODI, WEST INDIES v ENGLAND, Kensington Oval, Barbados (1330 GMT).