The alleged bomber blew himself up after finding himself surrounded by police, destroying the building in which he took shelter.
The building collapse injured at least 11 people, including officials.
Police have also taken five others into custody for their alleged involvement in the plan.
Recent attacks in Saudi Arabia, the Gulf's most powerful regime, has mostly been carried out by the Islamic State, who has targetted the Shia community.
The regime is also an important ally of the US-led coalition, who's fighting against the IS.
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