He was 75.
He is survived by wife, a son and daughter.
Milkha Singh played four Test matches in the early 60s. His elder brother Kripal Singh, also played for the country, in 14 Tests. They played together in one Test against England in 1961-'62.
A flamboyant left-hand batsman and a fine fielder, Milkha Singh made his Ranji Trophy debut at 17 and played his first Test just after his 18th birthday.
He had a fruitful career for Madras (now Tamil Nadu) in the Ranji Trophy. He scored over 4,000 runs in first-class cricket inclusive of eight centuries.
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His nephew Arjan Kripal Singh played Ranji Trophy for Tamil Nadu and memorably scored a triple century in a game against Goa in 1987. He was involved in a massive partnership in that match with W V Raman, who too scored a triple hundred as the team piled up 912.
Expressing his condolences, former India captain Bishan Singh Bedi wrote on Twitter: "Once the most attacking left hand batsman o his times AG Milkha Singh is no more..AG clan is diminishing..RIP Micky..Guru MEHR Kareh..!!"
Veteran coach M K Iqbal, a close associate, said Milkha Singh was a stylish batsman, who served the state team for a long time and guided several young cricketers.