The 25-year-old from Durham was England's best paceman in the 178-run loss against Pakistan in the second Test in Dubai, claiming five wickets in the match.
The England and Wales Cricket Board confirmed on Friday that he would miss the final Test, saying that he needed to rest.
Reports suggested Wood would undergo surgery on the problem at some point, meaning he would face a lengthy layoff.
Wood is likely to be replaced by Yorkshire seamer Liam Plunkett although allrounder Chris Jordan could also be in the picture.
England will also drop wicket-keeper batsman Jos Butler to bring in middle-order batsman James Taylor for his first Test in three years.
Jonny Bairstow will keep wicket in the absence of Butler.
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