The French carmaker said the Aulnay plant near Paris, which employs 3,000 workers, would stop production in 2014.
Last week, Peugeot said its first-half sales had fallen 13% amid a “profound crisis” in its eurozone markets.
Another plant, at Rennes in western France, is set to shed 1,400 posts from the 5,600 it employs there.
Another 3,600 jobs would be lost across all facilities in France.
Peugeot’s chairman, Phillipe Varin, said the situation was grave.
“I am fully aware of the seriousness of today’s announcement, as well as of the shock and emotions they will arouse in the company,” he said in a statement.
He said “the depth and persistence of the crisis” made the reorganization necessary and that workers who lost their jobs would receive support and help in finding new employment.
Around half of those currently employed at Aulnay would be offered new jobs at Peugeot’s other Paris plant at Poissy.
Unions described the announcement as a “declaration of war” and an “earthquake”, the AFP press agency reported.
In an interview with Europe 1 radio, French Social Affairs Minister Marisol Touraine said the cuts were “unacceptable”.
Peugeot’s sites are working well below capacity, with the average operating at 76% of their potential.
It said that the output of its smaller cars – which account for 42% of sales – was worse than average as many of its competitors operated in lower-cost markets.
The carmaker said it expected to report a loss for the first half of this year and to return to break-even by the end of 2014.
Earlier this year, Peugeot announced a 1bn-euro (£800m; $1.2bn) savings programme on top of headcount cuts of 6,000 announced last November.
Peugeot also this year entered into an alliance with GM of the US, under which GM takes a 7% stake in Peugeot, making GM the second-biggest shareholder in the French firm after the Peugeot family.
The company said the effects of that deal would not be felt until after 2014.
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