He is playing his first tournament since suffering serious injuries in a car accident in December 2022 that kept him out of last year's IPL as well as the 50-overs World Cup in India
Rahul had been due to return to the Indian starting lineup after recovering from a shoulder injury sustained during the home Test series against Australia.
"There are no major health concerns and he is making rapid progress, much to the satisfaction of the medical team," BCCI said in a statement.
"As a precautionary measure, he is advised further rest and hence will not be available for selection for the first Test match against Sri Lanka, which starts on July 26 at Galle."
Abhinav Mukund is expected to replace Rahul at the top of the batting order alongside Shikhar Dhawan.