The match officials' report raised concerns over the part-time off-spinner’s bowling action which was handed over to the West Indies team management.
This is the second time Brathwaite has been reported for a suspect bowling action. He was first reported in August 2017 but was cleared following an independent assessment.
He will be required to undergo testing by September 14 but is allowed to bowl in international cricket until the results are revealed.
India thumped West Indies by 257 runs in the second Test to win the two-Test series 2-0.