A police source said the victim was in distinctive Jewish dress. His life is not believed to be in danger.
Local police told BBC News the attack was "not terrorist-related".
According to the police source quoted by AFP news agency, the suspected attacker has a history of mental illness.
Alexandra Gonzalez, crime journalist for French digital TV channel BFMTV, tweeted (in French) to say that the injured man`s life was not in danger.
She also quoted a source close to the inquiry as saying that "no anti-Semitic motive had yet been established".
Strasbourg is home to a large Jewish community.
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