East Sussex Highways said Havelock Road is currently shut in both directions.
Scaffolding is being put in place and the road will remain closed until the area has been made safe, according to the council.
This is the second time the road has been closed due to falling masonry. Last Tuesday, bricks fell from Queensbury House and on to the pavement below.
The road was closed while police and the fire service attended the incident.
Then, on Tuesday evening (August 10), the road was closed again in both directions while further work on Queensbury House was taking place.
Last week bricks fell from the fifth floor of the building.
Stagecoach said most of its services within the town centre had to be diverted due to the falling debris.