The victim "was injured in the shoulder and chest," Turki said.
"Security was able to find the weapon used, which was a pistol (Glock) and the car used in the attack, as forensic evidence."
Turki added that the suspects "trained for two weeks" before the attack.
Denmark has confirmed that one of its nationals was shot and wounded in the Saudi capital Riyadh on November 22nd and dairy company Arla later said that the shooting victim is an employee of its subsidiary Danya Foods. The company reported that the man is recovering
The pro-Isis media group al-Battar Media Foundation released a video last week
purporting to show the shooting of the Danish man, US-based monitoring group SITE said.
The video shows an individual shooting from the backseat window of a vehicle at the driver of a white car on a highway in a desert area.
It identifies the driver of the white car as Danish citizen "Thomas Hopner."
Officials in Saudi Arabia have not identified the victim.
The Dane was driving away from work at a company in Riyadh's Al-Kharj Road area when he was shot, SPA reported.
Authorities have arrested the alleged gunmen, driver and videographer, Turki said.
A week after the incident, someone stabbed and wounded a Canadian while he shopped at a mall in Dhahran on Saudi Arabia's Gulf coast.
Several Westerners were killed in Saudi Arabia in a wave of Al-Qaeda violence between 2003 and 2007.
The latest arrests come as Saudi Arabia -- along with several other Arab countries -- takes part in US-led air strikes against Isis in Syria.
Canada and Denmark are among Western states taking part in a similar aerial bombing campaign against Isis in Iraq.
In November, Saudi Arabia blamed Isis-linked suspects for the killing of seven Shiites, including children, in Eastern Province.
Isis has declared a "caliphate" in parts of Iraq -- bordering Saudi Arabia -- as well as in Syria. It has been accused of widespread atrocities including the beheading of Western hostages.
The video claiming that Isis supporters attacked the Dane also carried an audio recording, allegedly of Isis leader Abu Bakr al-Baghdadi, saying that Saudi rulers will see "no more security or rest".
The kingdom is home to Islam's holiest sites and practises a strict version of Sunni Islam.