The Thursday evening blast was the latest incident in Qatif, which has seen rise in criminal violence as well as protests in the region.
Police spotted a stolen sports utility vehicle used "to carry out terrorist and criminal crimes" and then took "necessary action", a ministry statement said, without detailing what tactics police used.
"As a result, it caught fire and exploded," killing its two occupants.
"An investigation is underway to reveal the identity of those two individuals."
Police found firearms and ammunition, some of which exploded as a result of the blaze, the ministry said.
Footage that circulated on social media showed thick smoke rising from a vehicle engulfed in flames, with periodic sounds of explosions.