The country's power provider said the drone strikes hit a major power station in the Sudan port of Sudan, causing a "complete power outage."
Blasts and fires near the city's main international airports were reported as paramilitary forces targeted key cities for the third consecutive day.
The flight was cancelled after drones attacked international airports and attacked at a hotel near the current presidential palace.
A journalist, Cristina Karrer, told the BBC's Newsday program.
During the dawn period, smoke could be seen on the skyline of the formerly safe city, and thousands of civil wars fled refuge.
Sudan Electric Power said on Tuesday it is assessing the damage to its substation, which damaged the supply of water, health and other services.
Witnesses told AFP that one drone targeted a civilian area at Port Sudan Airport and another attacked the main army base in the city's center.
AFP reported that a third drone hit a "gas station near the southern port" in the densely populated city center, with UN officials, diplomats, aid agencies and Sudanese troops relocating from the capital Khartoum.
Witnesses said a major hotel near the residence of Army Chief Abdel Fattah al-Burhan was also attacked.
Mariam Atta, nutrition director at Port Sudan Children's Hospital, described the moment she first heard the attack.
"We woke up the roar of the explosion and felt fear. We had never seen an attack before, but we saw smoke rising and the fire - it was overwhelming."
Asked if she was concerned that the attack might happen again, she said:
"Yes, we are scared and likely to happen again. The fear is unchanged. As long as there is an intention to target the Port of Sudan and important areas and intimidate civilians, these attacks will continue."
UN Deputy Spokesperson Farhan Haq said the UN has temporarily suspended aid flights to the Port of Sudan after the drone strike, but regular aid operations continue.
Mr. Huck added: “None of our offices, houses or warehouses have been affected and we continue to operate regularly.”
Sudanese government spokesman Khaled al-Aiser said on Tuesday that the military is protecting the affected fuel warehouses “to the greatest extent”, adding that “the will of the Sudanese people will remain undestructible.”
The military blamed the Paramilitary Rapid Support Force (RSF) on a drone attack that began on Sunday. RSF has not commented on the attack yet.
The African Union warned in a statement that the attack on the Port of Sudan represents a "risk escalation" in the Sudan civil war and "a direct threat to the lives of civilians, humanitarians and regional stability."
Before Sunday's attack, the Port of Sudan avoided bombing and was considered one of the safest places in a war-revelling country.
The paramilitary group increasingly relies on drones to recover its lost territory, including Khartoum being withdrawn by the army in March.
The two-year battle between the Army and the RSF has killed thousands of people, forcing millions of dollars from their homes and causing the world's worst humanitarian crisis.
Both the Army and the RSF are charged with war crimes.
Other reports from Gladys Kigo