After a second-ball duck in England's tour opener last week against a Western Australian XI in Perth, Cook faced only 28 balls.
England are already coping with the loss of Steven Finn, who was ruled out of the Ashes tour after tearing the cartilage in his left knee ahead of the opening warm-up game.
The tourists also are planning to be without allrounder and fellow quick bowling option Ben Stokes for the looming Ashes series against Australia - he remains in England awaiting the outcome of a police investigation following a street-fight in Bristol.
England will be aiming to defend the Ashes when the five-test series starts November 23 at the Gabba in Brisbane, but Root's squad is conscious that the English were swept 5-0 on their last tour to Australia and are expected to be without star allrounder Ben Stokes.
The seriousness of Ball's injury is not yet known, with England confirming they will assess ankle overnight before deciding whether a scan is necessary.
Bowling around the wicket, Ball turned his back foot in his delivery slide and fell to the turf, before being helped from the field less than 10 minutes before the first adjournment in play.
Ball was considered a likely selection for the first Test in a four-pronged English pace attack featuring Jimmy Anderson, Stuart Broad and allrounder Chris Woakes.
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