The 46-year-old, who played 26 Tests and 198 one-day internationals for Australia from 1998 to 2009, was involved in a single-car accident outside Townsville in Queensland state on Saturday night.
Police said emergency services attempted to revive the driver and sole occupant, but he died from his injuries after the car left the road and rolled.
“Australian cricket has lost another of its very best,” Cricket Australia chairman Lachlan Henderson said in a statement.
“Andrew was a generational talent who was instrumental in Australia’s success at World Cups and as part of Queensland’s rich cricket history.