They say the attacker - who has not been identified - was shot dead by police. Two of the injured are in a serious condition.
The incident happened in the Opera district of central Paris.
Witnesses spoke of panic, as people tried to hide in restaurants and cafes from the streets. The motive for the attack was not immediately known.
The witnesses say police officers first tried to taser the attacker - but then fired two shots after this failed to stop the assailant, France24 reports.
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