South Africa was due to launch the joint exercises on Friday. It calls the drills routine but they have fuelled domestic criticism and fears they could endanger relations with Western partners.
The beginning of the exercises coincides with the first anniversary of the Russian invasion of Ukraine and follows Russian President Vladimir Putin's decision to suspend its last major nuclear arms control treaty with the United States.
The ship, named "The Admiral Gorshkov of the Fleet of the Soviet Union", had arrived at Richards Bay "performing the tasks of a long-range voyage", RIA reported, citing a statement from the Russian Northern Fleet.
The Gorshkov warship, which was sent off from Russia on Jan. 4, carries the Zircon missiles which have a range of 900 km (560 miles) and can travel at several times the speed of sound, making it difficult to defend against them.
In late January, the ship tested its strike capabilities in the western Atlantic Ocean.
