The Islamic State jihadist group claimed the June 26 suicide bombing of the Shiite mosque in Kuwait City, which it said was carried out by a Saudi.
One of the three suspects was detained in the Khafji area near the Kuwaiti border after opening fire on security forces, the interior ministry said in a statement carried by the official Saudi Press Agency.
"As result of the shooting, two security personnel were injured and rushed to hospital," the ministry said.
"Two of them were born in Kuwait and they have ties to a fourth sibling who is present in Syria as part of Daesh," the ministry said, using an Arabic acronym for IS, a Sunni extremist group that has seized large parts of Iraq and Syria.
Also Read
On Friday a Saudi policeman was shot dead during a raid in Taif, where officers said they found IS flags.
Three suspects were arrested. A fourth escaped but was later killed in a gun battle with law enforcement officers, the interior ministry said.
The IS-affiliated group calling itself Najd Province, which claimed the Kuwait bombing, also said it carried out two suicide attacks at Shiite mosques in eastern Saudi Arabia in May.
IS considers Shiites to be heretics and has targeted them across the region.
Gulf interior ministers on Friday held an emergency meeting in Kuwait after the string of bombings and called for coordination to confront what they called a "serious epidemic".