In a statement, departmental spokesperson Byron La Hoe said several rocks fell onto the road on the Noordhoek end "and caused significant damage to two catch fences and the road surface".
"Geotechnical engineers visited the site and put a remedial action plan in place," La Hoe added.
According to the statement, the road would be closed for three to four weeks. The road would be opened as soon as it was safe to do so.
"The area is very exposed to strong winds, and there is a high risk of rockfalls and mudslides down the steep mountain slopes," La Hoe said.
Motorists were advised to use Ou Kaapse Weg as an alternative route.
"Motorists can expect road closures on Chapman’s Peak Drive this winter whenever there are high-risk weather conditions."