Four or five people were caught on camera breaking into the Musee d'Orsay via a back door early on Sunday.
An alarm sounded but the apparently drunken group fled after punching a 10cm (four inch) hole in the famous painting Le Pont d'Argenteuil.
This is the latest in a number of security incidents at French museums.
The attack occurred on Paris's Nuit Blanche - an annual all-night festival of music and culture.
French Culture Minister Christine Albanel said the artwork could be restored but that this was an attack on French heritage.
'Criminal act'
The museum, on the Left Bank of the Seine in the French capital, houses a major collection of Impressionist works.
Ms Albanel said the gang had tried other doors before succeeding at the back door "even though it had big bolts".
She said: "It's always a heartbreak when an art object that is our memory, our heritage, that we love and that we are proud of is victim of a purely criminal act.
"We know there were four or five people, likely four boys and a girl, who entered around midnight to 0100, broke a door that was, perhaps, fragile."
No arrests have so far been made.
Le Pont d'Argenteuil, painted in 1874, is a view of the Seine with a bridge and boats.
Several recent incidents have highlighted security problems at French institutes.
In February a performance artist attacked a work by Marcel Duchamp at the Pompidou Centre.
Four paintings were stolen from the Fine Arts museum in Nice in August.
On Tuesday, a woman goes on trial accused of leaving lipstick marks on a Cy Twombly work on show in Avignon.
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