The England star, captain of the side while Michael Vaughan recovers from a knee injury, sustained a fresh injury to his problem left ankle during the third Test against Sri Lanka concluded at Trent Bridge on Monday, a match the tourists won by 134 runs to end the three-match series level at 1-1.
David Graveney, England's chairman of selectors, had been due to announce the One-day squad on Wednesday.
But an England and Wales Cricket Board (ECB) statement Tuesday said the squad would be revealed "later in the week at a time to be confirmed".
The statement added: "The England medical staff is awaiting further information on Andrew Flintoff's injured left ankle and an update will be issued tomorrow (Wednesday)."
England, who slumped to 190 all out at Trent Bridge after Sri Lanka off-spin ace Muttiah Muralitharan had taken eight for 70, then found themselves facing up to the prospect of Flintoff missing the one-dayers.
"I've had a scan which shows bone fragments - three of them," Flintoff said after Sri Lanka had won with more than a day to spare.
The hard-hitting batsman and fiery pace bowler has now suffered a recurrence of discomfort in the same joint which required surgery 16 months ago.
Flintoff's setback comes at a time as fellow England quicks Simon Jones (knee) and James Anderson (back) although Stephen Harmison is now playing county cricket with Durham after a shin problem.
"The film has gone to the specialist - so with respect to the NatWest Series or anything, there are no decisions," Flintoff added at Trent Bridge after Monday's close.
"At this stage it's just a case of waiting to see what the findings are. They've found these fragments - whether they've been around for a long time or are a new thing, I'm not sure."
If both Flintoff and Vaughan are ruled out, England will have a new captain.
The choice is likely to be between Marcus Trescothick, who has stood-in before, or his fellow left-handed opening batsman Andrew Strauss, formerly captain of Middlesex.
The one-day series starts at Lord's on June 17 with the other matches at the The Oval (June 20), Riverside (June 24), Old Trafford (June 28) and Headingley (July 1).