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.
The fact 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.
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