Denmark was chosen for the program because of its citizens' penchant for online shopping, according to a VW press release.
Customers can order their cars via Volkswagen's Danish website, and make payments with a credit card or smartphone-payment service.
Going through multiple models and variations can make buying a car online a tedious process. But VW’s trial will be simple and easy as consumers can only choose an Up with two different trim levels and a small number of optional items, because of the need to pre-stock cars for delivery.
Launched in 2012, the Up is a city car substantially smaller than Volkswagen's popular Golf hatchback.
Gasoline versions use a 1.0-liter turbocharged 3-cylinder engine, but VW also offers an e-Up electric variant.
Customers who buy their cars online must still take delivery at Volkswagen dealers.