The shooting took place in the French capital’s 10th arrondissement, police said.
A 69-year old man has been arrested in connection with the incident, the prosecutor's office said.
The motives of the gunman remain unclear, with two of the four injured left in a serious condition, the French officials said.
Paris police said they were dealing with an incident on the Rue d'Enghien and urged the public to stay away from the area.
One witness, a shopkeeper, said that seven or eight shots had been fired, causing mayhem in the street.
"It was total panic. We locked ourselves inside," the witness said.
This is a breaking story. More to follow. By Arthur Scott-Geddes , Telegraph