The Bureau of Meteorology warned people in the area to prepare to shelter.
"People between Cape Tribulation and Coen, including Cooktown, should complete preparations quickly and be prepared to shelter in a safe place," the bureau said on Monday.
The cyclone, which formed in the Coral Sea, crossed Queensland's northern coast, Cape York Peninsula, on Monday morning and is on a westward track.
Tiffany is forecast to emerge over the Gulf of Carpentaria on Tuesday morning.
Authorities are confident adequate measures are in place for Cooktown and Lockhart River.
"Our preparations are very good. We have high confidence in the shelters and the structures in the areas that are impacted," State Disaster Co-ordinator Steve Gollschewski said.
"We have factored into our planning the cases of COVID that are currently in the Cape and that is well covered in a our operational planning.
"Similarly for the emergency response that may need to come afterwards if we have loss of power, we have testing of those people in place before they go in, all of that is looking pretty good at this stage."
The bureau is warning communities to expect wind gusts of up to 130km/h as the system currently sits south of Coen, near Lockhart River.
Tiffany is expected to bring destructive winds and heavy-to-intense rain to communities in far north Queensland before moving and intensifying as it moves towards the Northern Territory coast.
Severe tropical cyclone coastal impact in the Northern Territory is possible on Wednesday or Thursday, the bureau says.
"People in far north Queensland communities will start seeing and feeling the effects of Tropical Cyclone Tiffany as it comes closer to the coast, which means an increased risk of flooding and some localised damage in these regions," senior meteorologist Dean Narramore said.
Premier Annastacia Palaszczuk said impacted residents should keep up to date with emergency alerts via the BOM.
Other parts of Queensland have already been struck by floodwaters with one person dead and a 14-year-old girl missing as waters begin to recede in Maryborough in the southeast.
A 22-year-old man's body was found in a submerged ute at Kanigan, north of Gympie, on Saturday, while water police, aerial support, divers and volunteers are searching for the girl who was swept away while fleeing a car caught in floodwaters on Saturday.
The remnants of tropical cyclone Seth dumped 600mm of water on the Wide Bay-Burnett region in two days, causing widespread flooding and an evacuation order for Maryborough's CBD.
Authorities had expected the river to peak in Maryborough above a major flood level of 10.5 metres, impacting about 80 homes on Sunday afternoon, prompting the evacuation.
The levee was protecting the CBD until an underground stormwater valve failed just before 2pm on Sunday, allowing floodwater to surge through the drains and into the streets.
A dozen pumps each moving about 120 litres a second appear to have kept the floodwaters at bay as the river peaked at about 10 metres late on Sunday night, the local mayor said.
But the BOM said flood waters are expected to drop back to moderate levels on Tuesday.
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