Jasper is forecast to reach high end category 4 intensity later on Thursday and possibly category 5 on Thursday night, the Bureau of Meteorology said in its latest forecast.
Over the weekend Jasper is likely to weaken but will remain as a tropical cyclone next week.
The "unusual" cyclone tracked south-southwest into the Coral Sea overnight.
"At this stage the highest risk of a cyclone impact is the region north of Mackay but the timing and severity of the coastal impact remains highly uncertain at this stage," the bureau said.
Jasper is not only the first tropical cyclone of the season but is also believed to be the first to form off Australia in December during an El Nino.
"It is rare to see a December cyclone let alone one where we do have El Nino," a bureau spokesperson told AAP.
"It is unusual to be seeing this. There aren't too many cyclones we have seen through the month of December let alone early December."
The bureau will issue regular updates to keep communities informed as the situation evolves over coming days.
It said the slow-tracking cyclone might provide plenty of time for communities to batten down the hatches before a potential impact.
Australia's cyclone season is usually from November to April, typically peaking in Queensland in February and March.
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