Gaekwad passed away in the western city of Baroda on Wednesday after suffering various health complications.
He played 40 Tests and 15 ODIs for India before becoming a selector and coach of the national team.
Gaekwad scored 1,985 runs from 70 Test innings, with a highest score of 201 against Pakistan in the 1982-83 series.
“My deepest condolences to the family and friends of Mr Aunshuman Gaekwad. Heartbreaking for the entire cricket fraternity,” Jai Shah, secretary of the Board of Control for Cricket in India (BCCI), said in a social media post.
Prime Minister Narendra Modi also expressed sadness over the batsman’s death.
“He was a gifted player and an outstanding coach. He was pained by his demise. Condolences to his family and admirers,” he wrote on X.
Gaekwad was known for fearlessly facing West Indies fast bowlers in an era when there were neither helmets nor restrictions on bouncers.
He had to undergo an operation after being struck on the ear by a Michael Holding bouncer that punctured his eardrum.