The group reportedly collected and moved horns under the guise of a trophy hunting operation.
Authorities have called on visitors to report suspicious activities this festive season.
The prince will deliver a speech denouncing the illegal wildlife trade at a conference in Washington.
Rangers in the park are working to protect endangered rhinos.
The park says it often moves rhino to other parks at this time of year to stimulate growth.
The Department of Environmental Affairs says 1,020 rhino have been killed, exceeding the numbers for 2013.