Officials say the man was carrying a knife and reports suggest he was wearing a fake suicide vest.
Minutes earlier President Francois Hollande had praised police in a speech commemorating the Paris killings.
Gunmen murdered 17 people in a series of attacks including at Charlie Hebdo and a Jewish supermarket.
In his address, Mr Hollande said 5,000 extra police and gendarmes would be added to existing forces by 2017 in an "unprecedented" strengthening of French security.
In addition, 2,000 extra jobs are being created in the intelligence services.
After his speech at the police headquarters in Paris news emerged about the shooting in the 18th district, in northern Paris.
French officials say the man shouted "Allahu Akbar!" (God is Great) outside a police station in Goutte d`Or, near Montmartre, where police shot and killed him.
He was wielding a knife and bomb disposal experts were brought in after wires were seen extending from his body.
A police robot checked the man`s body but a belt he was wearing contained no explosives, according to reports.
A year ago police shot dead three jihadist gunmen who inflicted three days of terror on Paris. But questions remain about their jihadist contacts and possible accomplices in the Middle East.
Three police officers were among the 17 victims of the gunmen on 7-9 January, 2015.
Charlie Hebdo anniversary: Suspect shot by Paris police
07 January 2016
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French police have shot dead a man who was apparently trying to attack a police station, on the anniversary of the Charlie Hebdo attacks.
