The spokesman said among them was the interior ministry website brought down for an hour on Wednesday after being targeted in a so-called denial of service attack from "hundreds of IP addresses in different countries".
The kingdom's information security centre has begun an inquiry into how to counter such attacks and reduce their impact on online services, he said in a statement.
In August, Saudi oil giant Aramco was the target of a cyber attack that the authorities said was aimed at halting production in the world's largest crude oil exporter.