The series is currently locked at 1-1 after England won the opening match in Hyderabad and India came back to win the second in Visakhapatnam.
“Leach sustained the injury during England’s first Test victory in Hyderabad and missed the second Test in Vizag as a result,” the England and Wales Cricket Board said in a press release on Sunday.
“He will fly home from Abu Dhabi in the next 24 hours, where the England team have been staying ahead of the third Test in Rajkot, which starts on Thursday (Feb 15). Leach will work closely with the England and Somerset medical teams in respect of his rehabilitation,” it added.
The ECB also confirmed that the team “will not be calling up a replacement” for Leach.