The State Security Agency said police raided three hideouts in the capital Riyadh and exchanged gunfire in one of them, the SPA news agency reported.
The people arrested were linked to the IS group, it said, without elaborating.
A man refused to surrender and blew himself up in a house in eastern Riyadh where explosive belts were being made, the statement said.
Police later exchanged gunfire with another member in an apartment and killed him. Five people were arrested in a third site.
Police said Wednesday’s raids had help foil fresh attacks in the oil-rich country which witnessed a series of bombings in the past months.
Since late 2014, IS has claimed a series of bombings and shootings against Shiites and security forces in the Sunni-majority kingdom.
Saudi Arabia is a member of the US-led international coalition that has been battling the Sunni extremist group in Syria and Iraq.