As a category three system, Fina passed between the Tiwi Islands and Darwin at the weekend, packing destructive winds and heavy rain.
Authorities toiled through Sunday night and restored power to 5000 homes and businesses, but around 14,000 were still without power on Monday morning.
Chief Minister Lia Finocchiaro acknowledged there was much work to be done to get Territorians back to normal life.
"When you look at the outage map, it is widespread, there are people who will be waking up this morning coming out of their second night with no power, and that has a huge impact," she told Channel Seven.
"We've had destructive winds, mass power outages and there's a big, big clean-up job to come."
A power team will be sent to the Tiwi Islands now it is safe to do so, Ms Finocchiaro said.
Of the NT's 153 government schools, 66 were impacted by the cyclone, with 15 closed on Monday.
The cyclone strengthened into Monday, in open waters above the Joseph Bonaparte Gulf, producing sustained winds of up to 185km/h, with gusts of up to 260km/h.
The Bureau of Meteorology's Jonathon How said the tropical cyclone was expected to gradually weaken by Monday afternoon, before it crossed the northern Kimberley coast later in the evening.
It was then likely to continue weakening.
Overnight rain totals were not as large as previous days as the cyclone was over open water.
Darwin had recorded 157mm of rain at the airport since 9am on Saturday, while Middle Point, southwest of the city, copped 393mm.
There were no reports of serious injuries or significant property damage on Sunday.
The BOM has a warning zone in place from Wadeye to Dundee Beach in the Northern Territory and the NT/WA border to Troughton Island, including Kalumburu in WA.
Gales with damaging wind gusts up to 120km/h were likely about coastal areas between Dundee Beach and Daly River Mouth extending to Wadeye if Fina takes a more southerly track.
They could hit parts of the northeast Kimberley coast from Monday morning between King George River Mouth and the WA/NT border and extend west to Troughton Island, including Kalumburu, overnight on Monday into Tuesday.
The bureau is warning of heavy to intense rainfall which could lead to flash flooding about coastal areas between Dundee Beach and the Daly River Mouth, possibly extending south to Wadeye.
The NT Emergency Service advises people from Dundee Beach to Daly River Mouth to remain sheltered in a safe place and to secure boats, outdoor furniture and playground items.