The infection is thought to have come from pork sausages called Rullepoelse, made by a firm in Hedehusene, near the capital Copenhagen. The product has now been withdrawn from sale.
So far eight other people have tested positive for listeria.
Deaths occur mostly among people who are already in a weak condition. The outbreak began last September.
Denmark's state health agency SSI says the outbreak is believed to be under control.
Health officials are trying to determine if any of the contaminated meat was sent to schools or restaurants, or was exported.
Listeria symptoms often include fever, headache, diarrhoea and vomiting. The incubation period can last two months, making it often difficult to trace the source of contamination.
Listeria can spread from delicatessen food even when kept cool in a refrigerator.