South Africa's health ministry said in a statement that "The source and linkage of cases remain under investigation," adding that there was a high probability of local transmission.
Health authorities say contact tracing is under way.
The country reported its first monkeypox case last week, a case that was also not linked to travel.
Monkeypox is a viral disease that causes flu-like symptoms and skin lesions. It is endemic in parts of Africa, but not South Africa.
More than 40 countries where monkeypox is not endemic have reported outbreaks of the viral disease, which spreads through close contact and was first found in monkeys.
Last week, the World Health Organization decided against declaring a global emergency over the rise of monkeypox. The WHO also plans to rename the disease to lessen the stigma associated with it, and its association with Africa.