The bomber detonated his device as security officers were breaking their Ramadan fast, al-Arabiya TV said.
Footage on the TV network showed a blazing vehicle. There are no details of casualties and no official comment.
The mosque is the burial place of the Prophet Muhammad and Medina the second-holiest city in Islam after Mecca.
State-linked Sabq news and the Okaz newspaper also carried reports of the suicide attack.
Earlier, at least one explosion rocked the eastern city of Qatif.
Qatif is home to many minority Shia Muslims and the blast appeared to target a Shia mosque. No casualties have been reported so far.
A suspected suicide bomber also died after detonating a device near the US consulate in the city of Jeddah. Two security officers were slightly injured as they tackled the man, but no-one else was hurt.
Social media footage from Medina showed a vehicle on fire in a car park, with two security officers lying nearby.
Other footage showed ambulances and police vehicles streaming to the area.
It is not clear who is behind any of the attacks.
The attacks come with the holy month of Ramadan drawing to a close and ahead of the Eid al-Fitr holiday.