The incident occurred about 8:15 a.m. Saturday as the man left a cafe called Europe in the Neustadt district of Dresden, police said in a statement.
It was revealed that he was also being investigated by authorities for the use of insignia of unconstitutional organizations, which includes Nazi symbols.
The American was detained by German police. The tourist, who sustained minor injuries, was apprehended by police, although the attacker fled the scene and remains at large.More news: Lukaku scores on United debut
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Earlier this month, two Chinese tourists were arrested and charged after photographing themselves doing Nazi salutes in front of the Reichstag in Berlin.
While residents of Germany and Austria, as well as many of their European neighbors, are educated on the laws forbidding Nazi symbols and expressions, it's not clear if Chinese tourists are aware of the post-1945 statutes.
A drunken tourist from the United States was beaten up by a passer-by in Dresden, eastern Germany, the local media said Sunday. "Don't do it anywhere in fact".