Emergency services said major flooding had particularly hit the northeastern city of Cairns, a tourist hub and gateway to the Great Barrier Reef.
The region's rivers were already saturated after a tropical cyclone battered the region this week, submerging highways and uprooting trees.
Amid the wild weather, a 10-year-old girl was in critical condition after being hit by lightning in south Queensland on Saturday.
Meteorologist Laura Boekel said Sunday that some areas of Queensland had seen more than 600 millimetres of rain in the previous 24 hours.
An additional 500 millimetres could fall over the next 24-hour period, she warned.
"The flash flooding is both dangerous and life-threatening as it can happen very quickly," she told a press conference.
With flood warnings issued for several areas, Queensland Premier Steven Miles warned that a weather emergency "was playing out".
"I have been speaking with people on the ground, who say they have never seen rainfall like this -- people who have lived in the state's far north for all their lives," he added.
"This is very serious and it could get worse."
Miles said rapidly rising water had closed Cairns Airport, which was expected to see flooding exceeding the record levels seen after a cyclone in 1977.
Around 10,500 people were without power across Queensland, Miles added.
Deputy police commissioner Shane Chelepy said there had been "multiple" evacuations and rescues. Five emergency centres had been opened.
There had so far been no reported deaths or missing people, he added.
The senior officer said some homes have been flooded, but gave no figures. The National Emergency Management Agency had been contacted for help, Chelepy added.
Acting Fire and Emergency Commissioner Stephen Smith said swift water rescue response units had dealt with more than 50 requests.
He warned residents to stay home.
"These are life-threatening events, we do not need people out and about," he said.
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