The bomber detonated his explosives after being stopped outside the Prophet's Mosque, a statement said.
The mosque is the burial place of the Prophet Muhammad and Medina the second-holiest city in Islam after Mecca.
Suicide blasts also struck two other Saudi cities on Monday.
That an attack happened in Medina at such a place is likely to leave Muslims around the world aghast, BBC World Service's Middle East editor, Alan Johnston, says.
Suspicion is likely to fall on so-called Islamic State (IS), he adds.
Meanwhile, the number killed in Sunday's bomb attack in Baghdad - said to be the deadliest there since 2007 - rises to 165, as Iraq vows to boost security.
(BBC News)