The police tweeted a photograph of the scene outside a courthouse as it warned that evacuations were taking place due to a second suspect vehicle in Northern Ireland's second city.
The digital version of the Belfast Telegraph reported that police were on the scene when the device went off outside the courthouse on Bishop Street shortly after 8pm.
They tweeted a picture of the car on fire after the blast, urging people to "stay away". On Facebook the police said: "As far as we know no one injured. There is another car we are not happy about. There are ongoing necessary evacuations," it posted.
It is understood officers were alerted to the bomb, giving them a 15-minute warning to evacuate the area before it went off.
Politicians from all sides on the island of Ireland condemned the incident.
Former Northern Irish first minister Arlene Foster, who heads the British province's Democratic Unionist Party, said: "This pointless act of terror must be condemned in the strongest terms. Only hurts the people of the city."
She said the swift actions of the emergency services had helped ensure there were no fatalities or injuries.
Naomi Long, leader of the Alliance Party, described it as “very disturbing news”.
Very disturbing news from L~Derry this evening. Hope that no-one is hurt. Police now reporting a second suspicious vehicle in the area.Naomi Long MLA (@naomi_long) January 19, 2019
Please follow police advice: avoid the area around Bishop Street Courthouse and stay safe while @PSNIDCSDistrict do their job. https://t.co/pOdpGGorjb
The three decades of sectarian bloodshed in Northern Ireland, known as the Troubles, were largely brought to an end under the 1998 Good Friday peace accords. Car bomb attacks were responsible for some of the worst atrocities.
Since the signing of the peace deal, there have been sporadic cases of violence.
In April 2018, petrol bombs and stones were thrown at police vehicles during a banned republican parade in Londonderry.
Also in Northern Ireland's second city, in February 2017 a bomb exploded outside the home of a police officer.