The gunman is still at large, they added.
The French Interior Ministry confirmed a "serious public security incident" in the city and urged residents to stay indoors.
The shooting is said to have happened close to a Christmas market in one of the central squares, Place Kleber.
Security officials have cordoned off the area and trams have been stopped, according to reports.
Eyewitness Peter Fritz told the BBC he heard gunfire and found a person who had been shot, lying on a bridge. He said he tried to resuscitate him but the man died.
