This is also Interior ministry officials in Baghdad, Iraq, say the number of people killed in Sunday’s suicide bomb attack in the capital has risen to 165.
In the Saudi Arabia blast, reports claim the bomber detonated his device as security officers were breaking their Ramadan fast, according to al-Arabiya TV.
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.
Meanwhile, the number of people killed in Sunday’s suicide bomb attack in the Iraqi capital, Baghdad, has risen to 165, interior ministry officials say.
The government has declared three days of mourning after the huge blast, which also injured 225 people.
A lorry packed with explosives was detonated in the Karrada district while families were shopping for the holiday marking the end of Ramadan.
It is believed to be the deadliest single bomb attack in Iraq since 2007.
Rescuers said whole families had been killed. Many people were badly burned.
So-called Islamic State (IS) has said it carried out the suicide attack.
Prime Minister Haider al-Abadi was greeted by angry crowds when he visited the mainly Shia Muslim area in the hours after the bombing.
His office said Mr Abadi understood the reaction of residents and would increase security by banning “magic wand” fake bomb detectors and improving vehicle inspections at roads into the city.
The fake bomb detectors, some based on cheap devices for finding golf balls, were sold in large numbers to Iraq by fraudsters.
One British businessman, who was jailed for 10 years, sold more than 6,000 devices to Iraq for up to $40,000 (£30,000) each.
The UK banned their export to Iraq in 2010 and several other fraudsters received prison sentences. Despite warnings that the devices were useless, the Iraqi security forces continued to use them.
Men continued to dig through rubble at the Karrada site on Monday, searching for the remains of those still missing.
Black banners were hung from nearby buildings bearing the names of victims and detailing their funerals.
In a statement on the attack, the Iraqi justice ministry said (in Arabic) that a group of prisoners convicted of terrorist crimes would be put to death in the immediate future.
The bombing at around midnight on Saturday came a week after Iraqi forces recaptured the city of Falluja from IS.
Reports said a refrigerator van had been packed with explosives and left near the popular Hadi Center.
“We need a number of days to be able to recover the bodies of victims. It is a difficult task,” a member of the civil defence forces quoted by AFP news agency said.
“The lists of victims I saw included whole families – the father and his sons, the mother and her daughters – whole families were wiped out by this explosion.”
A second bomb exploded shortly afterwards in another predominantly Shia area north of the capital, killing another five people.
The self-styled IS, which follows its own extreme version of Sunni Islam, said in an online statement that the attack in Karrada was carried out by an Iraqi as part of “ongoing security operations”.
The US said on Sunday that the attack strengthened its resolve to support Iraqi forces in their fight against IS.
UN Iraq envoy Jan Kubis said IS militants who had “suffered defeats at the battlefront are seeking to avenge their losses by targeting vulnerable civilians”.
BBC
