Incident in capital’s eastern district is the second attack on police force in in the kingdom in as many months.
Saudi Arabia has blamed the Islamic State of Iraq and the Levant (ISIL) group for the killing of two policemen in Riyadh earlier this month.
A statement released by the country’s interior ministry on Friday said one Saudi man had been arrested and a warrant had been issued for another.
Authorities said 23-year-old Yazid bin Mohammed Abdulrahman Abu Niyan had confessed to carrying out the shooting.
Abu Niyan told investigators he was following orders received from ISIL in Syria, the interior ministry said.
Three bomb-laden vehicles were also uncovered during the investigation, said the statement carried by the official Saudi Press Agency.
They also discovered machine guns, ammunition, money and several mobile telephones which revealed an exchange between the attackers and contacts in Syria, it said.
Authorities are offering a $267,000 reward for a second suspect, a Saudi named as Nawaf bin Sharif Samir al-Anzi.
The two Saudi policemen were killed in an April 8 drive-by shooting in an eastern district of the capital.
The ministry said that Abu Niyan had allegedly carried out the shooting while his partner, Anzi, drove the car and filmed the attack.
ISIL supplied them with the weapons, ammunition, and money to carry out the shooting through a “third party whom they did not meet,” the interior ministry said.
Al Jazeera’s Mohamed Vall, reporting from Jizan in Saudi Arabia, said authorities believe Anzi went by the alias ‘Berjis’, and had disguised himself by speaking with a North African accent of Arabic .
The Sunni-dominated kingdom is part of a US-led coalition taking part in an air war against ISIL, which has seized swathes of Syria and Iraq.
In March two police officers were injured in a similar attack, also in Riyadh.