"Kohli will miss some of the county games. It has not been decided how many games he will miss or whether it will be the whole month," said the senior Board of Control for Cricket in India (BCCI) official, speaking on condition of anonymity ahead of a formal announcement.
Indian media reports said Kohli had a disc injury and went to a Mumbai hospital on Wednesday, but the official said the star batsman "is suffering from fatigue."
The 29-year-old, who has one of the most intensive playing schedules in cricket and in January married Bollywood actress Anushka Sharma, signed up to play for Surrey in the English county championship for June before India start a tour of England in July.
The Mumbai Mirror said Kohli saw an orthopaedic surgeon on Wednesday who told him there was damage to spinal nerves and that he may have to miss part of the India tour if the injury worsened.
Kohli missed a one-day international during a recent tour of South Africa because of a strained neck.
Kohli was not available for comment and the BCCI made no immediate public statement.