The Buck Inn in Darlington, County Durham, posted the first ad on September 8 stating that it was holding a German night and using the line: "Don't Mention Ze War!"
The poster showed a black and white image depicting a uniformed Nazi soldier performing a Nazi salute with the right arm and a swastika on the left sleeve, while the text of the headline and the colour scheme resembled the "stylisation and colours typical of Nazi imagery", the Advertising Standards Authority (ASA) said.
The second post on September 12 showed that the Buck Inn had updated its Facebook profile picture to an image of a newspaper article about the German night poster, which was headlined "Pub's German night 'Nazi' poster criticised."
The pub also "liked" a number of comments, many of which contained jokes and puns in reference to the Holocaust, made by readers in relation to the posts.
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Three people complained to the ASA that the ads were offensive.
The Buck Inn said the original post was inspired by an episode of Fawlty Towers and was intended to be lighthearted and humorous.
The pub said the ad was not promoting the Nazi party and was not intended to "mock" the Second World War in any way.
It noted that the ad was seen on Facebook by more than 500,000 people, and said the fact that only three complaints were received indicated that most people had interpreted the ad in the way it had intended.
The ASA acknowledged the phrase "Don't mention the war" was a "fairly well known" quote from Fawlty Towers.
"However, we considered that the use of an image of a Nazi soldier wearing a swastika and performing a Nazi salute to advertise the pub's German cuisine night, in a humorous tone, was inappropriate and trivialised the events of the Second World War and actions of the German Nazi party," the ASA said.
"Furthermore, the ad appeared to link German culture intrinsically with Nazi Germany and the war."
It also found that the pub's "liking" of "distasteful" comments made in relation to the Holocaust by other users on its Facebook page was also likely to cause serious or widespread offence.
It ruled that the ads must not appear again, adding: "We told the Buck Inn to ensure that they did not cause serious or widespread offence by using Nazi references or imagery in their advertising, or by trivialising the events of the Second World War and actions of the German Nazi party.
"We also told the Buck Inn to ensure that comments made by other users on their Facebook page, which in themselves were likely to cause serious or widespread offence, were not 'liked'."
Buck Inn owner Craig Harker said: "This is political correctness gone mad. The world's gone absolutely bonkers if this is deemed offensive. It's a poster for a German night which was hugely successful.
"The regulars laughed it off and took the poster in the lighthearted, fun way that I intended. As long as business is good I'll continue to market my businesses however I see fit and let the PC brigade continue to do their jobs."