"We are not sure if this is a terrorist attack or only a personal crime," an Interior Ministry official said on Saturday, adding that the German worked for a Saudi catering company.
A Western expatriate quoted a witness as saying the man was gunned down when he left a supermarket in Riyadh at 6:15 pm (1515 GMT). "A car pulled up. They shot him in the head and body and escaped," the expatriate said.
Earlier this month, five foreigners were killed in an unprecedented attack on a petrochemical site on Saudi Arabia's west coast.
The Gulf Arab state, the world's largest oil exporter, has been battling a string of attacks linked to Usama bin Ladin's al-Qaida network since bombings in Riyadh last year killed 50 people.