The decision was made after the 26-year-old was sent for a scan following a recurrence of a bruised heel on Wednesday, which has plagued him throughout the current Test series.
Eoin Morgan will replace him as captain for the two-match T20 series and 22-year-old James Harris, currently with the England Performance Squad, will replace Broad in the squad.
The move caps off a miserable couple of months for Broad out in India, who failed to take a wicket in the two Test matches he played before being dropped for the third Test in Kolkata and missing the final Test through injury.
England will also be without Steven Finn, who is suffering from a lower disc strain, will also fly back to the UK.
The Middlesex paceman missed the final Test in Nagpur too, but is expected to return for the five-match One Day International series in January.
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BIOGRAPHY: Mohamed Salah