Bradman wore the "baggy green" cap during India's first tour of Australia as an independent country in 1947-48, scoring 715 runs in six innings at an average of 178.75.
During the five-Test series, Bradman also became Australia's first player to notch 100 first class centuries as he led the hosts to a 4-0 win.
At the end of the tour, Bradman gave the cap to the Indian team manager Pankaj "Peter" Gupta who passed it on to wicketkeeper P K Sen.
It was bought by the previous owner in 2003 and had been on loan to the Bradman Museum in the cricketer's home-town of Bowral since 2010.
Put up for auction with an estimated value of A$300,000-A$400,000, it sold to an Australian bidder, Sydney auction house Bonhams said.
Bradman's first Test cap worn in 1928 sold for A$450,000 in 2020, nearly a year after Australia's spin bowling great Shane Warne sold his baggy green for more than A$1 million to aid bushfire relief efforts.
Revered as the game's greatest batsman and one of Australia's best captains, Bradman retired after 52 Tests with a stratospheric batting average of 99.94, nearly 40 better than any other player with a minimum of 20 innings.
The sale of the latest cap has coincided with India's ongoing, five-Test tour of Australia, with the visitors leading 1-0 ahead of the second match starting at Adelaide Oval on Friday.
($1 = 1.5425 Australian dollars)
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