Eight other people were critically injured, while 14 were seriously injured and 44 others sustained minor to moderate injuries, the South Africa Broadcasting Corp. reported.
Transportation official Robin Carlise said there would be an investigation into the cause of the crash.
"Early reports from the surviving passengers indicated brake failure as the main reason for the crash," he said in a statement.
"The Provincial Regulatory Entity will investigate the legal status of the bus including the validity of the operating license, and whether the Certificate of Fitness is still valid."
He said the bus was owned by Atlantic City Liners.
Western Cape traffic official Kenny Africa said the bus was en route to Cape when the driver lost control and it veered off the N1 highway on the Hex River Pass, near De Doorns, the SABC said.
Another official said the bus was crushed up against the side of a mountain along the pass.