The group of about 160 scouts, aged 11-14, included a dozen teenagers from the Danish-speaking minority in northern Germany. The schoolyard was turned into a concentration camp with swastikas on the windows.
"I was shocked," Johanna Christiansen, a German woman, told the Ekstra Bladet newspaper on Thursday.
"It's wrong to expose children to this," said Christiansen, whose two daughters took part.
The local branch of the Danish Christian FDF scout organization organized the game last weekend at the Kongeaadal school, 260 kilometers (160 miles) southwest of Copenhagen.
Jes Imer of the local FDF chapter told the tabloid B.T. that they "may have crossed the line this time with a night game where Nazis chase Jews."
The schoolyard included a sign with the German words "Arbeit macht frei," or "Work will set you free," the infamous inscription over the entrance to the Auschwitz concentration camp in Poland.
"I don't know whether I should apologize," Imer told B.T., adding "I didn't want the game to hurt anyone."
None of those involved could be reached for further comment.