Queensland Police spokeswoman Chelsea Roffey said Maktoum died at the Palazzo Versace hotel. Foul play was not suspected, she said.
Maktoum maintained a low profile politically, allowing his younger brothers to run the daily affairs of Dubai, the BBC said.
His body was to be flown to Dubai on his private Boeing 747-400 Wednesday.
His brother, Crown Prince Sheik Mohammed bin Rashid Al Maktoum, succeeded him as ruler of Dubai, and declared 40 days of mourning.
Maktoum was also the vice president and prime minister of the United Arab Emirates, a federation of seven Gulf states.