The driver was a teenager on the run after killing his uncle. He triggered the blast after officers surrounded his vehicle south of the capital, Riyadh, on Thursday evening.
The bomber has been identified as Abdullah Fahd Abdullah al-Rashed. It said he was born in 1997 and had never travelled outside of the kingdom.
The dead uncle was identified also as Rashid Ibrahim al Safyan, adding that Safyan had been a colonel, without elaborating.
The Islamic State of Iraq and the Levant (ISIL) group has called on supporters to carry out attacks in the kingdom and killed 25 people in two suicide bombings at Shia Muslim mosques in the country's east in May.
"While security officers were manning one of the security checkpoints on Ha'er Road in Riyadh, they directed the driver of a suspected car to stop. The driver initiated an explosion which led to his death," the interior ministry said in a statement.
Reports said the teenage driver had killed his uncle that afternoon, and then ran off with his car.
The driver tried to drive bypass the checkpoint, then set off an explosive as security forces tried to surround him, it added.
