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 PK 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 $A300,000-$A400,000, it sold to an Australian bidder, Sydney auction house Bonhams said.
Bradman's first test cap worn in 1928 sold for $A450,000 in 2020, nearly a year after Australia's spin bowling great Shane Warne sold his baggy green for more than $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.
