The so-called multi-copter flew a few metres from the building to capture aerial footage of the building and well-wishers outside, according to an AFP reporter.
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.
Police were not immediately available for comment.