One of the 11 hurt is reportedly a tourist who was blasted in the stomach by the shooter, who is "known to cops for criminal activity" and now being chased through Strasbourg.
The city is now on total lockdown after the shooting, with police armed with machine guns on the street and people taking cover in bars and restaurants.
Security officials have cordoned off the market area and all trams have been stopped, according to reports from the scene.
The European Parliament was also placed on lockdown following the shooting with the orders "no one goes in, no one goes out."
The incident reportedly happened close to the world-famous market -which attracts two million tourists a year – in bustling Place Kleber.
"There were gun shots and people running everywhere," one local shopkeeper told BFM TV. "It lasted about 10 minutes."
Some of those on the scene reported they had seen victims lying on the street following the shooting.
A source at the prosecutor's office said the motive behind the gun attack was not immediately clear and that an investigation was under way to see if it was terror-related.
France's Interior Ministry said at least two people had been killed in the city, which is near the German border.
Regional authorities confirmed an "ongoing incident" in the city but gave no further details.
The interior ministry described the incident as a “serious security event” and warned the public to stay indoors.
Several sites in the city centre are concerned, it added, including rue des Orfèvres, rue des Grandes-Arcades and Grand'Rue.
Local journalist Bruno Poussard wrote on Twitter that there had been a dozen shots fired on his street in the city centre.
Emmanuel Foulon, a press officer for the European Parliament, wrote that there was "panic" following the sound of gunfire and armed cops were seen running through the streets.
Strasbourg deputy mayor Alain Fontanel tweeted: "Shooting in downtown Strasbourg. Thank you all for staying home while waiting for a clarification of the situation."
Yorkshire and the Humber Labour MEP Linda McAvan tweeted: "There's a shooting incident tonight in Strasbourg centre where Xmas market takes place.
"European Parliament on lock down. I and my staff are safe in the building."
Several other MEPs tweeted to say that both they and their staffs were safe and accounted for.
The European Parliament building is around two miles from the centre of Strasbourg.
Thorbjorn Jagland, the Secretary General of the Council of Europe, said on Twitter: "The police informed me tonight of a shooting in Strasbourg with possibly one victim and several wounded.
"The perpetrator is still on the run. This is a serious incident and I advise all staff and visitors to stay at home or indoors for the moment."
Strasbourg Christmas market is one of the oldest in Europe with 300 wooden chalets set up in the city's historic centre from November 23 to Christmas Eve.
It was being held amid tight security this year, with unauthorised vehicles banned from surrounding streets during opening hours and checkpoints set up on bridges and access points to search pedestrians' bags.
One of the biggest Christmas trees in Europe is put up in Place Kleber, the largest square in the city, which was named after French general Jean-Baptiste Kleber who was born in Strasbourg in 1753.
France remains on high alert after suffering a wave of attacks commissioned or inspired by ISIS militants in 2015 and 2016, which killed more than 200 people.
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