The explosion happened at 22:45 in Guildhall Square on Wednesday.
Police received information that the bomb had been left there and they had just an hour to evacuate the area.
There are no reports of any injuries. But it's understood there was minor damage to the building.
It is the second attack at the offices this year.
In January, a small explosion damaged a door of the building. Dissident republicans carried out that attack.
Foyle MP Mark Durkan said: "Thankfully no-one has been injured but those graces are no thanks to those who are behind this attack.
"They are out to destroy and they don't care if they injure or kill when they are at it.
"Derry is a city with many challenges and with many difficulties. But the City of Culture is one of the opportunities we have."