"This is a real slap in the face for concentration camp survivors and relatives of victims," conservative politician Gerda Hasselfeldt wrote in a letter to Amazon that was cited by Der Spiegel.
The 252-piece puzzle, being offered for $24.99, is sold on Amazon's American website as suitable for children aged eight and over, but it is not available for sale on Amazon's German website.
It shows a picture of two ovens at one of the two crematoriums at Dachau, where bodies of prisoners were burned.
Screenshot from Amazon website
Amazon's US media office did not immediately return a call seeking comment.
More than 200,000 Jews, gays, Roma, political opponents, the disabled and prisoners of war were imprisoned in Dachau during World War II. Between 32,000 and 43,000 people died in the Bavarian camp before it was liberated by US troops in April 1945.
"The Dachau memorial is a place of remembrance for the suffering of countless victims. It cannot be in Amazon's interest to sell such a game," wrote Hasselfeldt, parliamentary chief of the Christian Social Union of Bavaria, sister party of Chancellor Angela Merkel's Christian Democratic Union.