Tropical Cyclone Esther has developed into a category-one system in the Gulf of Carpentaria.
The system is forecast to cross the coast near the NT-Queensland border between Borroloola and Mornington Island on Monday.
"It's expected to cross pretty much on the line of the Queensland and Northern Territory border," BOM NT spokeswoman Jude Scott said.
"At this stage the cyclone track map does have the system passing pretty close to the Robinson River area.
"So we can expect to see gale-force winds sustained over a period of many hours in that area and also heavy rainfall totals, between 100 and 200 millimetres of rain in 24 hours."
The BOM issued a warning for Port Roper to Kowanyama, including Groote Eylandt, Borroloola, Mornington Island and Karumba.
Inland areas between Borroloola and Normanton, including Doomadgee, were also included in the warning zone.
Ms Scott said people in Robinson River would most likely start to feel the impacts of the weather system in the early hours of Monday.
"As this system crosses the coast, we can expect to see the weather start to deteriorate really overnight [Sunday night] for coastal communities."
Superintendent Daniel Shean, NT Emergency Services incident controller, said Robinson River was the focus for police but no evacuations were necessary.
But he said vulnerable people, including those on dialysis and older people, would be taken to Katherine or Darwin.
Widespread flooding from heavy rainfalls is also likely and a flood watch has been issued for Barkly and Carpentaria coastal river systems.
"That may lead to some roads becoming impassable in the coming days," Ms Scott said.
"Most areas in the Top End can expect to see some rainfall towards the end of this week."
Superintendent Shean said people in the affected areas should ensure their cyclone kits were well stocked.
"Ensure that you've got sufficient water and supplies for the next three days, know where you're going to stay during the weather event, talk to your friends and family, let them know where you're staying," he said.
"We would rather people don't drive - if you do drive and come across flooded roads, if it's flooded, forget it."
BOM's senior meteorologist in Queensland, Lauren Pattie, said damaging to destructive wind gusts with "short-lived" tornadoes in the Cape York Peninsula region could be expected to continue into Monday.
"Across the Peninsula, in particular with thunderstorms, we're seeing some tornadoes with some destructive wind gusts in them," she said.
"They're quite isolated, they're very short-lived."ABC