The Barron River is rising, with people in the Barron catchment and Machans Beach told to prepare, Cairns Regional Council said.
The river was predicted to reach 9.6 metres at Kamerunga Bridge around 1pm, the council said.
Queensland Premier Steven Miles has warned locals to be on alert and follow instructions.
He said 1977 flood levels are expected to be exceeded.
“We’ve seen rainfall in some places of almost 600mm with more to come,” he said.
Miles said locals have told him they have “never seen rainfall like this.”
“This is very serious and it could get worse,” he said.
He said 10,500 homes are without power.
Homes in Innisfail and around the Mossman River have been flooded – some for the second time this week.
“I think Queenslanders can be assured that our disaster systems are ready and well in place,” he said.
“I’m in constant contact with the those coordinating the disaster.”
Cairns Airport has now closed, after earlier warning of delays, bringing travel chaos a week before Christmas.
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“A further assessment will take place at 6pm.” the Airport said on Facebook.
Multiple people have been rescued, emergency services say, with people warned to stay off the roads.
After hitting the Queensland coast on Wednesday evening as a category 2 system, Jasper rapidly weakened into a tropical low as it made its way over the state.
Thunderstorms and heavy rains have continued to batter some areas however.
Laura Boekel from the Bureau of Mereology warned of “widespread and continuing rain”.
Black Mountain has seen 652mm over 24 hours, with many areas getting more than 300mm.
More than 20 places have had over a meter of rainfall she said.
Flash flooding as well as flooding from rivers are expected.
Another 500mm is possible over the next day.
Financial help was already rolled out as the cyclone hit last week.
Meanwhile, South East Queensland is expecting storms amid a heatwave.