Tugboats were trying to pull the 230m-long ship named Smart off a sandbank, National Sea Rescue said in a statement on Monday, adding that "the structural integrity of the ship was compromised".
The single-hull, 151 279-tonne ship is registered to Alpha Marine Corp and flies a Panamanian flag.
It was supposed to deliver its cargo to the Fangcheng port in China, according to Thomson Reuters data.
No injuries have been reported.
The Richards Bay port is on the Indian Ocean. This is the second cargo ship to run aground off South Africa this month.
The other was the 165m-long Kiani Satu, which hit ground off the southern coast. – Reuters