The fire broke out just before 6am on Sunday.
Authorities say the sprinkler system appeared to have been tampered with and so did not work. By afternoon, firefighters were still trying to contain the blaze in one of the several buildings that make up the parliament complex in the legislative capital, Cape Town.
There were no reports of any injuries.
A man in his 50s has been arrested inside parliament, Public Works and Infrastructure Minister Patricia De Lille told reporters, adding that the case had been handed over to an elite police unit called the Hawks.
"It's the role of the Hawks to investigate any attack on political institutions," De Lille said.
The cause of the blaze was not yet known but De Lille said that according to a report that she received, a standard maintenance fire drill had been conducted just before parliament closed for the Christmas and New Year holidays and everything, including the sprinklers, was working.
"What was discovered this morning is that somebody has closed one of the valves and so then there was no water to trigger that automatic sprinkler system coming on," De Lille said, adding that CCTV footage confirmed that somebody was in the building from the early hours of the morning.
President Cyril Ramaphosa told reporters after visiting the site that parliament's work would continue despite the blaze. He also praised firefighters for saving a "very important national asset of our government".
The parliamentary complex, some of which dates back to 1884, consists of a cluster of buildings. The National Assembly, or lower House of Parliament, is situated in what is known as the New Wing.
The upper house, or National Council of Provinces (NCOP), is located in what is called the Old Wing or Old Assembly, which is also used for committee meetings.
"The fire has been contained in the Old Wing. Firefighters are currently trying to control the fire in the New Wing, where the fire has affected the National Assembly Chamber," parliament said in a statement.
The roof of the old building had collapsed, and the fire has gutted the third floor of the building, including office space and the gymnasium, local authorities say.
The parliament's fire alarm only rang when firefighters were already on site.
By afternoon smoke had partially subsided after billowing for hours from the roof and entrance of the National Assembly, but the fire is still active, and is now concentrated on the first and third floor.
