“In light of the so-called Volkswagen affair in the US and Europe, where (the company) has admitted extensive cheating, Økokrim wants to investigate whether any crime has been committed in Norway and whether the fraud has had any effect on the cars imported to this country,” the economic crimes unit said in a statement.
Volkswagen, the world's biggest car manufacturer, admitted on Tuesday that as many as 11 million of its diesel cars worldwide were equipped with software capable of fooling official pollution tests.
The scandal, which broke in the US, pushed VW's chief executive Martin Winterkorn to announce his resignation.
Norwegian police said they would cooperate with customs and transport officials in its investigation. It did not indicate the type of penalty Volkswagen could face.
Diesel is not very popular in Norway, a country generally mindful of the environment and with a large number of electric cars.
According to Norwegian media, VW has sold fewer than 20,000 diesel cars in Norway per year the past five years.
Volkswagen Norway has in recent days told local media that it does not know whether rigged models were sold in the country.