Kohli has scored nearly 9,000 runs in 113 test matches.
"Virat has spoken to Captain Rohit Sharma, the team management and the selectors... certain personal situations demand his presence and undivided attention," BCCI said in a statement.
"The BCCI requests the media and fans to respect Virat Kohli's privacy during this time and refrain from speculating on the nature of his personal reasons," it added.
India host England in a five-match series starting on Thursday in Hyderabad.
The England squad arrived at the venue on Monday.