The gates of the courthouse and a security hut were destroyed in the attack which is thought to be the work of dissident republicans opposed to the peace process.
Most of the roads near the courthouse have reopened to traffic, although New Street remains cordoned off. Diversions have been put in place. Windsor Hill Primary School in Newry will remain closed to pupils on Wednesday.
Mark Simpson, BBC Ireland correspondent
The Newry bomb attack is the most serious incident involving dissident republicans in Northern Ireland since the recent political breakthrough at Hillsborough Castle.
The dissidents are making it clear they want to wreck any political progress.
Politicians at Stormont will be disappointed and disgusted at the bomb attack - but they won't be surprised.
Gradually in recent weeks, the dissidents have been stepping up their activities.
Since they tried to kill a Catholic police officer, Peader Heffron, in Co Antrim last month, they've targeted three police stations in Co Armagh and now they've exploded a bomb in Co Down.
By striking in three different counties, they are trying to increase the range and intensity of their violence.
But they still have very little support and a limited amount of weaponry. Without that, they cannot mount a full-scale campaign.
Chief Constable Matt Baggott rejected suggestions that the police and the government had become complacent about the threat posed by dissident republicans.
"We have put many more police officers back on the streets, we are continuing to invest in the right capabilities and technology to tackle the dissident threat, and we are fully behind the devolution of power to Stormont, because again that's about the political consensus that we need," he said.
Chief Superintendent Robinson said: "We didn't get any calls warning of the bomb until 10.20pm which was from a third party.
"That stated that we had around 30 minutes to clear the area. The explosion went off at 10.37pm which was 17 minutes later.
"At the time we were still clearing the area. But for the fact there was divine intervention, there could have been multiple casualties."
Later, the US Secretary of State, Hillary Clinton, condemned the car bomb and insisted it would "not destabilise the peace process".
"I strongly condemn the bombing last night, it was another cowardly act of violence by those who would prefer to plant bombs than to argue for votes and participate in the political process," she said.
"The parties in Northern Ireland have similarly condemned that action in the strongest terms and I urge that everyone continue to work towards seeing the devolution of authority and a better future for Northern Ireland."
The attack comes days after a mortar bomb was abandoned near a police station in the village of Keady, about 20 miles away.
It is thought to be the first time a large car bomb has exploded in Northern Ireland since the bombing of Stewartstown police station in 2000.
In the last few years a number of large car bombs been have planted but have either failed to detonate or only partially detonated.
There have also been several attacks with smaller under-car bombs such as the one which almost killed a police officer in County Antrim in January.
BBC NI Home Affairs correspondent Vincent Kearney said police had been bracing themselves for some kind of response to the Hillsborough Agreement, signed just over two weeks ago.
"The fact that it has taken them so long to respond tells us something about their capabilities," he said.
Prime Minster Gordon Brown's official spokesman condemned the attack.
"Such acts are entirely unrepresentative of the views of the vast majority of people in Northern Ireland ... we will not allow a tiny minority to turn the clock back," he said.
Sinn Fein MP for Newry and Armagh Conor Murphy said: "The fact that we're in the process of devolving policing and justice powers and there's an attack on a courthouse will not be lost on people.
Chief Constable Matt Baggott said that there was 'absolutely no excuse' for the bomb attack
"These people are trying to drag us backwards and ensure we have the British army back on the streets."
DUP MLA William Irwin said the bomb was "a cowardly action by those who want to drag Northern Ireland back to the past".
SDLP MLA Dominic Bradley said: "People are saying that they got enough of this sort of thing during the Provo campaign, it was wrong and senseless then and it is wrong now."
Ulster Unionist assembly member Danny Kennedy said the bomb was "proof of a deteriorating security situation in Northern Ireland".
"It represents a clear attack on security services and government institutions. It shows a very worrying level of capability that these dissidents now have."
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