"There were gunshots and people running everywhere," one local shopkeeper told BFM TV. "It lasted about 10 minutes."
Local journalist Bruno Poussard said he heard more than a dozen shots being fired along the street where he lives before soldiers and police descended on the scene.
France's Interior Ministry confirmed a "serious public security incident" and said at least two people.
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."
European Parliament press officer Emmanuel Foulon described panic as the incident unfolded. He was one of a number people understood to have taken cover in bars and restaurants.
He wrote on Twitter: "Several people on the ground. We remain hidden since the first shots."
MEP Richard Corbett said he was in a restaurant in the city when shots "were fired" and the restaurant was "not letting anyone in or out".
Local authorities in the Grand-Est and Bas-Rhin region tweeted for the public to "avoid the area of the police station" close to the city's Christmas market.
Security officials have cordoned off the area and trams have stopped running.
Thorbjorn Jagland, the secretary general of the Strasbourg-based 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."
"Shooting in downtown Strasbourg. Thank you all for staying home while waiting for a clarification of the situation," Strasbourg deputy mayor Alain Fontanel.
French President Emmanuel Macron is being kept informed of unfolding events, his office said.
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 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.
A source at the prosecutor's office said the motive for the shooting was not immediately clear and that an investigation was under way to see if it was terrorism-related.
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