Public Works and Infrastructure Minister Patricia De Lille described it as "a sad day for our democracy".
She added that the fire was currently burning in the National Assembly chamber, but had been contained in other parts.
There were no reports of any injuries in the fire, according to De Lille.
The cause of the blaze was not yet known.
Jean-Pierre Smith, a Cape Town mayoral committee member responsible for safety and security, said it appeared the fire detection system appeared not to have worked properly.