Fødevarestyrelsen (Danish Veterinary and Food Administration) said oysters are from Lemvig.
The agency has closed the area in Lemvig for commercial harvest of mussels and oysters and is monitoring it.
It warned consumers not to collect seafood in the area.
Noroviruses can cause gastroenteritis in people an illness that usually includes diarrhea and/or vomiting. People with illness usually develop symptoms of gastroenteritis within 24 to 48 hours but symptoms can start 12 hours after exposure.
People became sick at the beginning of November. The contaminated batch of oysters has been withdrawn and discarded.
Illnesses can be avoided if oysters are cooked to an internal temperature of 90° Celsius/194° Fahrenheit for a minimum of 90 seconds.