They were posted to the Whinhall True Blues Flute Band’s Facebook page, but have now been taken down.
Ephraim Borowski, the director of the Scottish Council of Jewish Communities, said the photographs should be “condemned in the strongest terms”.
Mr Borowski added: “The meticulously planned industrialised murder of six million people solely on the grounds of their ethnicity is not a joke, and neither is anything that glorifies those who planned it.
“Racism, including racism against Jewish people – antisemitism – must always be condemned in the strongest terms, and we would urge the Orange Order to do so.”
Taken in 2013, one of the photographs shows a man dressed as Hitler, with a female companion clearly dressed as Eva Braun. Two children stand in front of them, wearing rags and yellow stars - similar to those Jewish people were forced to wear in Nazi Germany.
The Herald reported that a comment posted on Facebook underneath the photograph read: “Congratulations to our joint winners!!!”
The Grand Orange Lodge of Scotland have been approached for comment.
