"Closing the factory is the only option after five years of unsuccessful negotiations," said a French-language statement issued by Goodyear Dunlop Tires France.
It added that the plan had been presented to a works committee and would be the basis of talks with workers' representatives.
Chairman Henry Dumortier said: "We are fully aware of the impact of the announcement we are making today and the plan's heavy consequences for staff, their families and local communities."
He added: "We are deeply disappointed that five years of negotiations were not enough to reach a compromise with representatives of workers at Amiens Nord. Today's announcement was the only option left to us."
Production of low-end tyres for passenger vehicles and farm equipment at the plant resulted in a loss in 2011 of 61 million euros, according to Goodyear figures.
The decision was taken against a background of weaker demand for vehicles which threatens 20,000 jobs in France.
In addition to Goodyear, automakers Peugeot Citroen and Renault have announced restructuring programmes which could result in almost 19,500 job losses by 2016.
Franck Jurek, a leader of the CGT trade union at the Goodyear plant, said: "We have been battling for six years against 400, 800, 1,200 job cuts, we are going to keep fighting."
A new works committee meeting was scheduled for February 12, the CGT said, while forecasting a big turnout by workers.
Goodyear said that closing the tyre plant was a decision "aimed at remaining competitive in the tourism and agricultural sectors."
French President Francois Hollande had paid a visit to the Amiens factory during his electoral campaign, calling for more workers rights, in cases where companies were still making profits.
Amiens Mayor Gilles Demailly, a member of Hollande's Socialist Party, called Goodyear's decision "unacceptable" and said he wanted to meet with Industrial Renewal Minister Arnaud Montebourg to discuss what had become a "national issue."
"Announcing the plant's complete closure is even worse than we could have imagined," said Demailly, before warning that the city's industrial zone "will be largely decapitated."
The CGT vowed to mobilise Goodyear workers from all over France for the next works committee meeting, which is to take place at the group's French headquarters in Rueil-Malmaison, west of Paris.
Accusing the Goodyear management of "lying right from the start," CGT leader Mickael Wamen said staff at the Amiens site would be on strike on February 12, and "we will come here with all of Goodyear's workers."
He claimed that "Goodyear has no legal chances" of closing the tyre plant.
On Tuesday, a French appeal court suspended the Peugeot restructuring plan that concerns 8,000 jobs because the group had not fully informed staff representatives at its auto parts unit Faurecia of the plan's details.