Zandile Mafe denied the charges against him.
Officials have described the fire, which severely damaged parts of the parliament precinct, as an attack on South African democracy.
The legislature has played a crucial role in helping roll back repressive apartheid-era policies over the past three decades, and parts of the parliament complex date to the 1880s when South Africa was under British colonial rule.
Mafe “did not satisfy the court that exceptional circumstances exist which in the interests of justice permit his release”, the court in Cape Town ruled, according to a video posted by a TimesLIVE reporter on Twitter.
Another news website, Eyewitness News, reported that Mafe would appeal Friday’s judgment.
(Writing by Alexander Winning, editing by Mark Heinrich).