The England and Wales Cricket Board said vice-captain Ollie Pope would lead the team in the match at The Oval starting Thursday, with England 2-1 up in the series.
Allrounder Stokes has struggled with various fitness issues in the four tests against India so far, during which he has sent down 140 overs the most he has bowled in any series.
The 34-year-old, who is the leading wicket-taker on either side with 17 scalps, has injured his right shoulder, his bowling arm, and it is understood he could need up to 10 weeks to recover.
"I am obviously disappointed to not be able to finish the series," an emotional Stokes told reporters on Wednesday.
He added: "I have got a decent tear of one of the shoulder muscles I can't pronounce.