The accused, identified only as Roland T, was to face court on Thursday for allegedly teaching his black mongrel sheepdog – suspiciously named Adolf - to perform the controversial trick on command.
But a spokesman for the Berlin justice department said on Wednesday the charges had been dropped because it was not clear whether the 54-year-old had broken the law with his dog's "salute".
He added the man was still facing a number of other charges due to his use of Nazi symbols.
Roland T, who lives in Lichtenrade, southern Berlin, will still be tried for allegedly wearing a T-shirt with a picture of the Nazi dictator and shouting pro-Hitler slogans on previous occasions.
Pictures in the German newspaper Bild have shown the accused with a short, Hitler-style moustache.
Nazi symbols and gestures, including words and actions which can be interpreted as promoting Nazism, are illegal in Germany where the genocidal Hitler-era dictatorship remains a sensitive subject.