Mr Mubarak, 82, is in hospital after reportedly suffering heart problems. His detention order will be in place for 15 days, state TV reported.
His sons Alaa and Gamal have also been detained amid allegations of corruption and violence, police say.
Mr Mubarak stood down in February after a popular uprising against his rule.
Since then, tens of thousands of protesters have staged weekly Friday protests in Cairo's Tahrir Square, demanding that he stand trial.
About 800 people are thought to have been killed during the protests, as police opened fire and cracked down on the crowds.
There are also widespread allegations of corruption and abuse of power under Mr Mubarak's 30-year rule.
