The 34-year-old was replaced by Shikhar Dhawan in the team for the third test which the visitors won to narrow England's lead to 2-1 after three matches of the five-game series.
Wrist-spinner Kuldeep Yadav was sent home to play for India A team in two four-day matches against Australia A.
The 18-year-old Shaw earned his maiden test call-up on the back of a string of strong performances for India A, including a knock of 188 against West Indies A last month.
Vihari has been one of the most consistent performers in domestic cricket, averaging 59.79 in 63 first-class matches.
Off-spinner Ravichandran Ashwin retained his spot in the squad despite struggling with a hip injury during the third test.
The fourth test begins on Aug. 30 at the Rose Bowl in Southampton.
Full squad: Virat Kohli (captain), Shikhar Dhawan, KL Rahul, Prithvi Shaw, Cheteshwar Pujara, Ajinkya Rahane, Rishabh Pant, Dinesh Karthik, Hardik Pandya, Ravichandran Ashwin, Ravindra Jadeja, Jasprit Bumrah, Ishant Sharma, Mohammed Shami, Umesh Yadav, Shardul Thakur, Karun Nair, Hanuma Vihari.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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