Authorities said Chekatt entered the perimeter of the famed market, one of the oldest in Europe, by the city's Corbeau Bridge and started shooting at passers-by on the Rue des Orfèvres around 8 p.m., when many were in the middle of their Christmas shopping.
Three of the injured have left hospital and three others are fighting for their lives, French media said on Thursday night.
Cherif Chekatt was killed in the Neudorf/Meinau area of the city after a police operation was launched around 9pm Thursday local time about two kilometres from where he launched his attack on Tuesday.
Chekatt has known ties to extremist groups, officials said.
Interior Minister Christophe Castaner told lawmakers in Paris on Wednesday that the gunman was injured in an exchange of fire with soldiers who were patrolling the Christmas market as part of regular anti-terror operations.
Authorities published Chekatt's picture late Wednesday with police describing him as risky and urging people not to approach him.
Police said they have identified the shooter, who has not been captured.
At least 245 people have been killed in terror attacks in France since 2015, according to an AFP toll.
French authorities have reportedly "neutralized" the gunman who opened fire at a Christmas market in Strasbourg earlier this week.
A French police official said security forces, including the elite Raid squad, took action based on a "supposition only" that Chekkat could be hiding in a nearby building.
A top French officials says a suspect has been killed in a shootout with police in Strasbourg. His parents and two brothers are already in custody.
Strict vehicle restrictions, security checks and patrols by armed police and soldiers amid the revellers have become the norm.
Asked whether police had been instructed to catch Mr Chekatt dead or alive, Mr Griveaux told CNews television: "It doesn't matter". He said Chekatt was armed with a handgun and a knife.
A wanted poster has been issued for Chekatt - a Strasbourg local who shouted "Allahu Akbar" before launching his gun and knife attack. "They replied", Castaner said.
Italian Interior Minister Matteo Salvini said one Italian was among the wounded, in critical condition.
A view shows an empty alley of the traditional Christkindelsmaerik (Christ Child market) closed the day after a shooting in Strasbourg, France, Dec. 12, 2018.
Three people were killed in the market attack, including a Thai tourist named by the embassy in Paris as Anupong Suebsamarn, 45.
The attack came as President Emmanuel Macron sought to take back control of the nation after a month of anti-government protests that have spread violence across the country.