Two police officers were injured in the attack, which President Emmanuel Macron called an "Islamist terrorist act".
The suspected perpetrator, identified as a 37-year-old Algerian-born man, was arrested on the spot. He was on a surveillance list for terrorism and was subject to a deportation order.
Three more people have been arrested in connection with the incident, according to the prosecutor's office, without going into details about their connection to the suspected perpetrator.
According to prosecutor Nicolas Heitz, the 37-year-old has "a history of mental illness" and France's Interior Minister Bruno Retailleau, who visited the police station in Mulhouse on Saturday evening, said that France had repeatedly tried to deport him from the country, but Algeria had refused to cooperate.
A 69-year-old Portuguese man was killed in the attack and two police officers were seriously injured. One of them has been discharged from the hospital.
