Several live power lines are down, according to NT Police and Emergency Services after the storm passed over the city just before midday on Saturday.
Trees were also brought down throughout the Greater Darwin region by the high-speed winds, and some are yet to be cleared.
Regional Controller Warren Jackson said in a statement: “It’s only been several hours since the cyclone passed.
He added: “While assessments of damage are undertaken, it is safest for community members to stay home.”
NT Emergency Services crews have started responding to over 400 calls for help in the aftermath of the cyclone.
Crews have placed clearing debris around the airport and Royal Darwin hospital as priority.
Mr Jackson said: “Don’t take unnecessary risks – only travel if it is absolutely required.”
Shelters were opened across the city and emergency services told residents to stay inside until the storm had passed.
The NT regional controller pointed to the damage visible across the city and warned of the potential consequences of stronger cyclones.
He said: “This is a real wake-up call for Darwin, given that was in what we’d say was the lower end — but it was a category two — you can see there was a significant amount of damage with trees fallen, houses have been damaged … a significant amount of rain has fallen in a short period of time which flooded roads … but as a result of that people still didn’t heed our warnings.”
Saturday’s storm also affected Darwin’s water supply. Residents have been advised to boil drinking water until advised otherwise.
One Darwin resident said: “Marcus sure packed a punch.”
Earlier in the day as the storm struck, water police rescued an elderly couple and two others from two boats that collided after one of them slipped its moorings in Sangove Creek.
The category two storm is now making its way towards the Timor Sea and is expected to hit Western Australia’s Kimberly Coast on Sunday, with wind speeds of up to 120 km/h.
Flights in are out of Darwin were cancelled on Saturday but flights are expected to resume and operate as scheduled on Sunday, according to Darwin International Airport.