“Good news: The Arla employee who was shot and injured in Riyadh on Saturday was operated on today [Monday, ed.]. The operation went well and he is now recovering,” Arla spokesman Theis Brøgger wrote on Twitter.
“It is still to early to say anything about the motive for the shooting but we are in close contact with the authorities on that,” he also wrote.
Arla has said that there is no reason to believe that the shooting was directly related to the company but has opted to increase security measures.
The Dane was driving away from work at Arla subsidiary Danya Foods in Riyadh's Kharj Road area when he was shot in the shoulder from "an unknown source", Saudi Press Agency said.
The rare incident comes after Saudi Arabia, the United Arab Emirates, Jordan and Bahrain in September joined a US-led campaign of air strikes against the Isis extremist group in Syria, raising concerns about possible retaliation in the kingdom.
Attacks on Westerners have been rare in the oil-rich kingdom in recent years, after several were killed in a wave of al-Qaeda violence between 2003 and 2006.
In October, a Saudi-American former employee of a US defence contractor shot dead one American colleague and wounded another in Riyadh.
The suspect had recently been fired from his job, officials said.