Tuesday's attacker had "never showed any sign of radicalisation," he told RTL radio, but stressed that the investigation was at an early stage.
Castaner said it "is very difficult to anticipate" attacks when they were staged by people who were not on the police radar.
But he said the police response was "immediate and effective."
The 22-year-old officer sustained minor neck injuries in the assault, which comes with France on high alert after jihadists killed seven people in London on Saturday.
Documents found on the attacker identified him as a 40-year-old Algerian who was a doctoral student in information science at a university in the east of France.
The suspect later claimed to be a "soldier of the caliphate" of IS, according to a source close to the investigation.
The policeman's colleague opened fire on the man, hitting him in the chest in panicked scenes around the Gothic cathedral that is one of France's most visited tourist attractions.
Watch: Witnesses to Notre Dame attack ran away after shots heard
Notre Dame attacker 'pledged allegiance to IS in video'
The video pledging allegiance to the jihadist group was found in a police search of an apartment he was renting in Cergy outside Paris, the source in the investigation said.
The man was placed in custody in hospital, where he is being treated for a gunshot wound to the chest.
Government spokesman Christophe Castaner told RTL radio on Wednesday that the attacker had "never showed any sign of radicalisation".
The attack comes as France is on high alert after jihadists killed seven people in London on Saturday.
France is still under the state of emergency imposed after the November 2015 attacks in Paris, when Islamic State jihadists killed 130 people in a night of carnage at venues across the city.
Watch: French minister on Notre Dame attack
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