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.
Australia took control of the second Ashes Test after the third day following a lower-order batting fightback and then taking six England wickets before the close of play.
Australia went to stumps on the second day of the pink ball Ashes Test on 378-6, the home side leading England by 44 runs on the first innings with four wickets still remaining.
Will Jacks is set to make his first Test appearance in almost three years after England named their starting XI for the second Ashes encounter against Australia that starts in Brisbane on Thursday.
England captain Ben Stokes has come out and said he will accept criticism for his team's performance in the first Ashes Test but has pushed back at jibes that the tourists are "arrogant".
