Police received the complaint from Andrew Dale, of Countesthorpe, who said the cards were obscene and rude.
Leicester shopkeeper Stuart Delahoy said he moved the card display to ensure it was discreet and private.
The cards at the shop in St Martin's Square in Leicester, which have swear words and sexual references, were not meant to be offensive, he said.
"It is modern day take on the Bah Humbug approach to Christmas"
"Most people take the cards in good humour and enjoy our take on Christmas," said Mr Delahoy.
He said there was no intention to take a jibe at Christianity but the cards were a humorous sideswipe at the "commercialisation" of Christmas.
"It is modern day take on the Bah Humbug approach to Christmas."
Mr Dale said: "They are obscene and just not on really - Christmas is about love and the hope that Jesus brings for resurrection and salvation - these messages are undermining that message.
"They shouldn't be displayed in a shop window where anyone can see them, including children."
"There is rude and there is obscene - but these were just the wrong side of funny."
Mr Delahoy said the police had talked to him about the cards.
Leicestershire Police said an investigation was ongoing but no criminal proceedings were under way.
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~43~RS~)