French president Francois Hollande confirmed the closure on Saturday and said his government intends to move the 9,000 occupants to reception centres across France.
Half of the Calais camp was dismantled in March but its population has since doubled.
Hollande said the Calais camp was "not acceptable" and "extremely difficult" for refugees fleeing war zones.
The announcement, which was made while Hollande visited one of Frances's 164 migrant reception centres in the city of Tours, comes as work has started on a UK-funded £1.9 million wall at Calais aimed at preventing migrants from boarding lorries heading to the port.
The actions of migrants attempting to enter the UK at the French port have caused continuing problems for haulage operators and also led to major disruption earlier this month caused by protests against the site.
Hollande, who is to visit Calais on Monday, insisted that "we cannot have such camps in France" and added that his country must show it is "capable of being dignified, humane and responsible".
The camp has become a symbol of his government's failure to tackle Europe's migrant crisis, and a target of criticism from conservative and far-right rivals seeking to unseat him in France's presidential election next year.
The closure plan will see 40 to 50 people being held at each of the reception centres in regions across France for up to four months while authorities investigate their cases.
Those who do not seek asylum would be deported.
This has prompted vehement protests from many local conservative and far-right politicians, saying they fear the consequences of having migrants in their towns.
Hollande has indirectly criticised that resistance and called for more solidarity, noting that neighbouring Germany has taken in a million migrants compared to the only 9,000 being relocated from Calais.