Five elephants were killed in the Vlakteplaas area of the park, and nine rhinos in the Stolznek region.
The South African National Parks Corporate Investigative Service is working closely with the Endangered Species Unit of the South African Police Service, and several more arrests are expected soon.
The horns of the rhinos have allegedly been sold for traditional medicine purposes.
Meanwhile, SA Parks Chief Executive, Mavuso Msimang, has denied allegations that important information regarding poaching incidents in the park has been withheld from the Convention on International Trade in Endangered Species (CITES), in order to enhance the country's chances of selling off its stockpiled ivory supplies.
Earlier, it was announced that Cites had approved the sale of the park's ivory supply to selected buyers in a few countries, and to use the proceeds to finance conservation projects.