Kohli pulled out of the first two tests, also for personal reasons. The Indian cricket board said in a statement that it fully respected and supported the player's decision.
The former captain, who has scored nearly 9,000 runs in 113 tests, will miss an entire home series for the first time in his career.
England won the opening test by 28 runs in Hyderabad before the hosts levelled the series at 1-1 with a 106-run victory at Visakhapatnam this week.
The third test will be held in Rajkot from Thursday, with matches to follow at Ranchi and Dharamsala.
The injured duo of batter KL Rahul and all-rounder Ravindra Jadeja, who missed the second match, were recalled to the 17-man squad announced by the BCCI for the final three tests. They will only play subject to fitness clearance from the medical team.
Middle-order batsman Shreyas Iyer was left out amid reports that he had suffered a back issue, while selectors resisted the temptation to rest in-form pace bowler Jasprit Bumrah, who has had his share of time out due to injury last year.
India squad: Rohit Sharma, Jasprit Bumrah, Yashasvi Jaiswal, Shubman Gill, KL Rahul, Rajat Patidar, Sarfaraz Khan, Dhruv Jurel, KS Bharat, Ravichandran Ashwin, Ravindra Jadeja, Axar Patel, Washington Sundar, Kuldeep Yadav, Mohammed Siraj, Mukesh Kumar, Akash Deep.