The season's first cyclone is a category 1 system, located about 300km east of Cairns.
It is expected to re-intensify into a category 2 cyclone by Tuesday afternoon as it moves slowly toward the coast.
Cyclone Jasper is tracking to impact landfall at Port Douglas north of Cairns at Wednesday lunchtime.
It may even become a category 3 system by the time it crosses the coast, the Bureau of Meteorology warned.
"If the system is slower and crosses on Wednesday night or early Thursday morning there is a slight chance that it will intensify into a category 3 before crossing," a bureau spokesperson told AAP.
"That's just something we will be keeping an eye on today."
In the meantime heavy rain and wind will be "ramping up" in the far north on Tuesday.
Gail force winds of up to 120km/h are expected to develop along the Queensland coast between Cape Flattery and Townsville.
"Going into tomorrow we've got destructive winds of up to 140km/h expected to develop between Wujal Wujal and Innisfail from early on Wednesday," the spokesperson said.
Gail force winds are expected to move inland as the cyclone crosses.
"Cyclone Jasper will weaken as it heads inland on Thursday. It will be heading towards the Gulf of Carpentaria, continuing on a westward trajectory," the bureau said.
⚠�🌀Tropical cyclone — Bureau of Meteorology, Queensland (@BOM_Qld) #warning continues between Cooktown and Townsville, and a Watch area extending north to Cape Melville and inland. Gales forecast to begin on Tuesday. Landfall on Wednesday between Cooktown and Innisfail. Details and updates: https://t.co/FBmpsInT9o pic.twitter.com/6wYALYDbTKDecember 11, 2023
Evacuation centres have been set up in Cairns, Port Douglas and Cooktown.
A cyclone watch zone is also in place, extending inland and further north to Cape Melville.
Preparations are well underway in the far north where there are fears up to 500mm of rain will fall in some areas.
Sandbags have been provided in Cairns where about 15,000 properties are at risk of storm surge flooding with a king tide predicted.
The Cairns hospital is also vulnerable, prompting contingency plans including sandbagging and the cancellation of elective surgery on Wednesday to free up capacity.
A nearby aged care facility may also be evacuated.
Cairns airport remains operational but a number of airlines have indicated there will be schedule changes or flight cancellations.
About 40 police officers and additional SES crews have travelled to the far north to help.
"It's been over 60 years since we've had a direct hit," Cairns mayor Terry James said.
"The roads will be cut off, potentially the power will be cut off. We tend to lose our power with a lot of rain and the onslaught of a cyclone."
Mr James urged locals to stock up and be prepared for up to five days without power.
About 450 Energy Queensland staff have been deployed to Rockhampton and Townsville in preparation to respond to potential power outages.
All national parks and campsites north of the Daintree River have been closed.
People have also been urged to avoid road travel throughout far north Queensland.
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