Sheik Maktoum, who also was vice president and prime minister of the United Arab Emirates, died at the exclusive Palazzo Versace hotel on the Gold Coast, a resort in eastern Queensland state, Queensland police spokeswoman Chelsea Roffey said.
The emir, a horse racing aficionado, arrived in Australia on Dec. 28, apparently for a world-renowned yearling sale known as the Magic Millions.
Authorities in Dubai would not give a cause of death. Australian police would only say the emir did not die of suspicious causes.
Australian media speculated that Sheikh Maktoum died of a heart attack, while the al-Jazeera satellite television broadcaster said he was believed to have "previously suffered from heart problems."
The emir immediately was succeeded by his younger brother, the crown prince, Sheik Mohammed Bin Rashid Al Maktoum, who is the defense minister of the United Arab Emirates and a high-flying businessman and breeder of race horses, said Deputy Information Minister Ibrahim Al Abed. The succession was automatic under the constitution.
The new emir, Sheik Mohammed, is known as the intellectual architect of Dubai's building boom.
Authorities at Australia's Brisbane Airport scrambled Wednesday to prepare the emir's private Boeing 747 jet to fly his body home in time for a Muslim burial within 24 hours of his death.
Dubai declared 40 days of mourning, with government offices shutting down for seven days beginning Wednesday. The stock exchanges in Dubai and Abu Dhabi ceased trading, and many shops and businesses closed.
Dubai TV interrupted its programs to show a picture of the sheik smiling with the voice of a Muslim cleric reading verses of the Quran, Islam's holy book.
"The United Arab Emirates today lost a historical leader who devoted his life to establishing the United Arab Emirates and enhancing its structure and the welfare of its people," the government said.
The secretary general of the Arab League, Amr Moussa, expressed his condolences, praising Sheik Maktoum for his "defense of Arab and Islamic causes."
Sheik Maktoum was born in the family home in Shindagha, near the mouth of Dubai Creek, and educated at a British university. He succeeded his father in October 1990 as ruler of Dubai, one of the seven constituent emirates of the UAE.
He tended to leave the day-to-day government of Dubai to his younger brother, but he took an active interest in the Emirates' foreign policy. He often represented the country abroad during the years when the former president, Sheik Zayed bin Sultan Al Nahyan, was ailing.
When Sheik Zayed died in November 2004, Sheik Maktoum became acting president for a few hours until the new leader, Sheik Khalifa bin Zayed Al Nahyan, was proclaimed president.
Sheik Maktoum's foremost interest was horse racing, and he and his younger brother worked to put Dubai on the world racing map. They founded the British-based Godolphin Racing, one of the world's most successful stables, and frequently said they aim to win the Kentucky Derby.
In Dubai, the authorities said Sheik Maktoum's funeral would be Thursday, and he will be buried at Umm Hurair cemetery in Bur Dubai.
Deputy Information Minister Al Abed said the country's Supreme Council, which comprises the rulers of the seven constituent emirates, will meet to choose a vice president to replace Sheik Maktoum.
The president then will nominate a new prime minister who, after being approved by the council, will form a new Cabinet.