Crumlin Road will remain closed overnight between Agnes Street and Carlisle Circus, and police have advised motorists to avoid the area.
A police spokeswoman said they were expecting some traffic delays during rush hour on Friday morning.
The courthouse, which was the venue for hundreds of paramilitary trials, closed in June 1998.
An underground tunnel links one of the docks to a former jail on the opposite side of the road.
The original architect of the Grade B listed building was Sir Charles Lanyon, who was also involved in the construction of some of Belfast's landmark buildings including City Hall, Custom House, Belfast Castle and Queen's University.
These pictures were taken by a BBC rooftop camera as firefighters tackle the blaze.
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