A man attacked passers-by with knives at a covered canal market in Mulhouse, near the German border, on Saturday afternoon, Michele Lutz, the local mayor, said in a post on Facebook.
Several police officers who intervened were injured, she said, adding: "The terrorist track seems to be favoured for the moment.".
One person has been killed and several have been injured, including police officers, in a knife attack in eastern France.
The suspect was arrested, according to BFM Alsace - which also reported that the public prosecutor said the man is on file for the prevention of terrorism.
President Macron called it an "Islamist terrorist attack" in comments to BFMTV.
