Residents took shelter as the category 2 storm hit, with many evacuating their homes as winds about 100km/h uprooted trees and brought down powerlines.
The intensity of the storm was reduced to a tropical low late on Wednesday night and it was due to continue to weaken as it moved inland.
But life-threatening flash flooding was still expected, with the state's far north facing up to 300mm of rainfall over six hours and 500mm in 24 hours.
The Aboriginal community of Wujal Wujal near Cape Tribulation, lay directly in the path of the storm as it reached the coastline.
An emergency warning was in place from Cape Melville to Cardwell as the system approached the coast, with people told to stay away from big windows.
Tropical Cyclone Jasper has brought down trees as it crosses the coast in far north Queensland. (HANDOUT/MYPOLICE GREATER CAIRNS)
"The heaviest rain is associated with these bands on the southern flank in that onshore flow," the Bureau of Meteorology's Sarah Scully said.
There was a risk the system could re-intensify into a tropical cyclone as it hits the Gulf of Carpentaria on Friday.
"There's a lot of uncertainty and it's highly dependent on how long that tropical low remains over those warm Gulf waters," Ms Scully said.
Prior to the system reaching the coast, more than 17,000 homes and businesses were already without power.Â
People from Cape Flattery down to Cairns were on Wednesday afternoon told to take shelter.
"Go to the strongest, safest part of the building you are in. This will be away from big windows," the emergency warning said.
"Stay there. Emergency services cannot get to you because it is too dangerous."
Local cafe owner Anton Rafferty told AAP people were mainly staying off the streets in Cairns.
"For the most part, people are just sitting at home waiting it out," he said.
Tropical Cyclone Jasper has caused flooding on the north Queensland coast. (HANDOUT/MYPOLICE GREATER CAIRNS)
Deputy Premier Steven Miles travelled to Townsville on Wednesday to monitor the emergency response.
The Australian Defence Force was also on stand-by to assist if necessary.
"We stand ready to support far north Queensland, the Queensland government and local governments in any way needed in the days ahead," federal Emergency Management Minister Murray Watt said.
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