Danish Defense Minister Soeren Gade said he was "saddened by this new tragedy."
"They were on patrol and were hit by a very powerful bomb placed on the roadside," Gade told Denmark's TV2 News.
The three Danes were to have ended their mission in August.
A total of 24 Danes have been killed in Afghanistan since Denmark deployed troops at the end of 2001, giving the Scandinavian country the highest per capita death rate among NATO forces in the war-torn country.
Denmark has more than 700 troops in Afghanistan, most of them stationed in Helmand province under British command.