The fast bowler will miss all three matches against the West Indies, starting at Edgbaston on 29 May, with England saying in a statement "he will be reassessed over the next fortnight to determine when he may return to action".
Lancashire's left-arm seamer Luke Wood, who had already been named instead of Archer for the T20I series that follows in June, has been added to the ODI squad.
The injury could also rule Archer out of a possible return to red-ball cricket where he was pencilled in to play for the England Lions against India A next month.
The 30-year-old has been hampered with back and elbow injuries since he last played Test cricket for England in February 2021.
The ODI and T20 series against West Indies is significant as Harry Brook's first since being named as England's permanent new white-ball captain.
England squads for West Indies
ODI: Harry Brook (c), Gus Atkinson, Tom Banton, Jacob Bethell, Jos Buttler, Brydon Carse, Ben Duckett, Tom Hartley, Will Jacks, Saqib Mahmood, Jamie Overton, Matthew Potts, Adil Rashid, Joe Root, Jamie Smith, Luke Wood.
T20: Harry Brook (c), Rehan Ahmed, Tom Banton, Jacob Bethell, Jos Buttler, Brydon Carse, Liam Dawson, Ben Duckett, Will Jacks, Saqib Mahmood, Jamie Overton, Matthew Potts, Adil Rashid, Phil Salt, Luke Wood.
England allrounder Jamie Overton has been ruled out of the remainder of the white-ball series against West Indies after sustaining a fractured right little finger during the first ODI at Edgbaston.
Brian Bennett scored Zimbabwe's fastest ever Test century but England were still well on top after two days of the historic one-off fixture at Trent Bridge in Nottingham.
England head coach Brendon McCullum has confirmed that seamer Sam Cook will make his Test debut against Zimbabwe at Trent Bridge on Thursday.
Captain Ben Stokes is "very confident" he can fulfill his role as an all-rounder in England's Test team ahead of a busy home schedule as he returns from hamstring surgery.
