Prison authorities said the video, broadcast late yesterday, is in response to "rumours" that al-Saadi Gadhafi is being tortured in custody.
Al-Saadi was extradited to Libya earlier this month from Niger, where he had taken refuge as his father's regime crumbled in 2011.
The Libyan government is preparing to prosecute him for his alleged role in trying to suppress the uprising against Gadhafi's rule.
In the video, al-Saadi is seen wearing blue prison uniform, sitting in what looks like an office. He says he is sorry for the "harm and disturbances", without elaborating,and says he is being treated well in prison.