An interior ministry spokesman also named a suicide bomber who killed four security officers near a mosque in the sacred city of Medina as Naer Muslim Hamad, a 26-year-old Saudi man.
The ministry said he had a history of drug abuse.
Three people who allegedly carried out attacks in Qatif were also named. Their nationalities are not clear.
Their names were given as Abdulrahman al-Omar (23), Ibrahim al-Omar (20) and  Abdulkarim al-Husni (20). The ministry said none of them had Saudi IDs.
The attacks in Qatif took place on the same day and were also suicide bombings.
A man died in Jeddah on Monday when attempting to detonate a bomb.
No group has claimed responsibility for the attacks yet but they are suspected to have been the work of people with allegiances to so-called Islamic State.
Saudi officials say 12 out of 19 people arrested over Monday's three bomb attacks in the country are Pakistani.