The interior ministry said 16 men and one woman were arrested. They were mostly Saudis but also included one Yemeni, an Egyptian and a Palestinian.
De-classified transcript: Guantanamo inmate believes Saudi royal had role in 9/11
They are the latest arrests connected with the Sunni extremist group in Saudi Arabia.
Since late 2014, IS has claimed a series of bombings and shootings targeting Shiites in the Sunni-majority kingdom, as well as the security forces.
Dozens of people have been killed, largely in Eastern Province, which is home to most of the country's Shias.
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"Months-long efforts culminated in the foiling of a terrorist plot that was to be carried out by a network made up of three cluster cells connected to IS," the ministry said in a statement to the official Saudi Press Agency.
"They targeted security officials and security, economic and military establishments and citizens in different locations."
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