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 fast bowler Mark Wood says he wants to up his intensity as he builds up to put himself in the selection frame for the first Ashes Test that starts in Perth on 21 November.
Laura Wolvaardt played one of the all-time great ODI innings to guide the Proteas Women into the ICC Women's World Cup final after a comprehensive 125-run victory against England.
England fast bowling legend James Anderson has been knighted for his services to cricket.
New Zealand battled past England by four wickets at Bay Oval on Sunday in the first match of their three-game ODI series, with half-centuries from Daryl Mitchell and Michael Bracewell proving pivotal.
