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Wood damaged his shoulder attempting to save a boundary on the fourth evening of the Second Test at Lord's, before England fell to defeat.
He bowled on the final day, and at good pace, but appeared troubled by the injury.
The ECB have described the problem as a "jarred right shoulder" but Wood hopes to be back for the Fourth Test at The Kia Oval, which begins on September 2.
Wood is having a solid series, with five wickets at an average of 28, but his loss will be particularly keenly felt due to the extent of England's injury list.
Jofra Archer and Olly Stone are out for the rest of the year, Stuart Broad for the rest of the summer, and Ben Stokes indefinitely as he
manages his mental wellbeing and a hand injury.
Chris Woakes is also out with a bruised heel but is expected to play for Warwickshire Second XI this week and also hopes to also be back in time for the Fourth Test.
Wood's injury means a Test debut for Saqib Mahmood — who has had a fine summer in the white-ball formats — is highly likely as England look for a pacy edge to their attack.
Craig Overton is the other spare bowler in the squad, but he could come in for Sam Curran.
Dawid Malan is also set to return for his first Test in more than three years, batting at No3, with Haseeb Hameed opening after Dom Sibley was dropped.