The attack happened yesterday in the Al-Ahsa region, the Saudi Press Agency said, citing a provincial police spokesman.
One member of the police force received "a minor injury" and five vehicles were damaged, the spokesman added.
"Authorities started criminal investigations," he added.
Most of Saudi Arabia's minority Shiites live in the kingdom's Eastern Province which includes Al-Ahsa, an oasis region where much of the kingdom's oil reserves are located.
In January a suicide bomber attacked a Shiite mosque in Al-Ahsa, killing two people and wounding seven during Friday prayers.
IS has also claimed attacks on Saudi security forces, most recently early this month when a police colonel was shot dead in the Riyadh area.
Residents have told AFP that criminal activity including the drug trade has also been linked to attacks on police in the east.
Earlier this year unrest including gunfire, burning tires and explosions shook the eastern town of Awamiya after the execution of prominent Shiite cleric Nimr al-Nimr on January 2.
