Police have identified the suspect as Strasbourg-born Cherif Chekatt, who was known to the intelligence services as a potential security risk. The country’s deputy interior minister said it was believed that the attacker had been injured by security forces on Tuesday night but that could not be verified.
Officials said that five people have also been detained.
Meanwhile, Interior Minister Christophe Castaner said on Wednesday that the gunman had eluded a police dragnet and was on the run, raising concerns of a follow-up attack.
The mayor of Strasbourg Roland Ries said that if possible residents should stay at home, but he added, they should also carry on with their lives despite the attack.
A spokesperson for the French Bishops described last night's events as a "horrible act". Monsignor Olivier Ribadeau Dumas in a tweet also said, that their thoughts were with "the families of the victims who have been so hard hit and to those who are fighting for their lives."
France raised its security threat to the highest alert level, and has strengthened border controls. Officials also said that German police have tightened border controls across the Rhine river.