Inspector Tanya Lesh said the group gathered on top of the Sentinel Mountain peak above Hout Bay.
“The group of about 100 people moved down the mountain to a nearby hotel and started throwing stones at the police,” Lesh said.
“The police retaliated by firing rubber bullets.”
No injuries were reported and no arrests were made. Two privately owned cars were damaged.
The protesters had dispersed by yesterday afternoon.
A recent report in the Sunday Times said the 321m-high Cape Town landmark in Hout Bay had come to the attention of a short list of celebrities and tycoons, including Oprah Winfrey, Sol Kerzner, and Donald Trump Jnr as well as the Bill and Melinda Gates Foundation.
The new owners could, if they wished, name the peak after themselves as The Sentinel was not a registered trademark.
Auctioneers had reportedly turned down two offers, including one for R15-million, after the property had been bought for only R60000 in 2005.
The protesters said the mountain belonged to the indigenous people of South Africa and could not belong to a private owner.