Middle-order batsman Craig was the youngest player to play Test cricket for Australia when he debuted in 1953 at 17 years and 239 days.
He then became the youngest Australian Test captain when he took over aged 22 years and 194 days.
He was made captain for the 1957-58 tour of South Africa despite having played in only six Tests and not being an established member of the team.
Craig played 11 Tests between 1953 and 1958, averaging a disappointing 19.88, before retiring when he was 26.
"We were very sad to learn of Ian's passing and on behalf of Cricket Australia, I extend our deepest sympathies to his family, friends and former teammates at this difficult time," the governing body's chairman Wally Edwards said in a statement.
"Ian earned a very special place in the proud history of our game as the youngest Australian to make a first-class double century, gain Test selection and captain his country.
"Beyond those remarkable achievements I will always remember him as a true gentleman.
"He will be sadly missed and will forever be remembered as one of the elite few to have captained his country in Test cricket."
Craig made his first-class debut for New South Wales in the 1951-52 Australian season, aged only 16.
Craig earned comparisons to Don Bradman after becoming the youngest player to score a first-class double century with an unbeaten 213 for NSW against the touring South Africans in January 1953, gaining his Test call-up for the last match of the series.
Ian Craig is survived by his wife Ross and three children.
Image: Ian Craig
Photograph: Central Press/Hulton Archive/Getty Images
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