It happened on Saturday afternoon. There are no reports of any injuries.
Bedford Street is expected to stay closed until about 18:30 GMT.
By coincidence, the street had been closed since Saturday morning to allow filming to take place for a BBC drama series.
The popular crime thriller staring Adrian Dunbar and Vicky McClure is now in its third series.
Bedford Street in Belfast city centre has been closed after glass fell from Bedford House onto the street below.