A man attacked people at a canal market in Mulhouse, near the German border, at around 4pm.
Prosecutors said a 37-year-old Algerian man – who had reportedly been on a terror watchlist – had been arrested.
“Horror has just gripped our city,” mayor Michele Lutz said on Facebook.
President Macron told BFMTV it was “beyond doubt” it was an “Islamist terrorist attack”.
He said interior minister Bruno Retailleau was heading to Mulhouse and would speak later.
The attacker is said to have been at a police station – where he was due to sign a document for his detention – but refused and ran into the market area where he launched the attack.
One police officer was stabbed in the neck and another in the chest, according to French media. Three other police sustained very minor injuries.
The knifeman had been under house arrest, Le Monde reported.
The attack comes a day after a stabbing attack by a 19-year-old Syrian refugee at Berlin’s Holocaust memorial.
A Spanish tourist was badly injured but had emergency surgery and is expected to survive.
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