After it landed, police took the pilot, who is believed to work for a local film company, into the hospital building for questioning.
Mandela has been in intensive care with a lung infection for three weeks in the Mediclinic Heart Hospital in Pretoria.
Radio-controlled aircraft are seen as a potential powerful tool to gather images from areas inaccessible to journalists, but the devices also raise questions about privacy.
On Thursday, Mandela's oldest daughter Makaziwe slammed the "crass" media frenzy around her critically ill father, likening the press to vultures.
Police were not immediately available for comment.