Authorities must work "methodically and with perseverance... to definitively close the camp", Bernard Cazeneuve told security forces in the city.
The minister said the dismantling would be "gradual and controlled" but that its closure should be achieved "as rapidly as possible".
Calais mayor Natacha Bouchart had earlier said that Cazeneuve assured her that the complex would be dismantled in a single operation, adding later that he had said it would happen before the end of the year.
France has made repeated efforts to shut down the camp of tents and temporary shelters, which authorities say is currently home to nearly 7,000 migrants following a surge of new arrivals in recent months.
Charities helping the migrants in the camp say the real figure is as high as 10,000.
The migrants gather in Calais hoping to smuggle themselves aboard lorries crossing the Channel to Britain either through the Channel Tunnel or on ferries.
Earlier this year, authorities cleared shelters in parts of the site in a bid to persuade migrants to move into more permanent accommodation or camps elsewhere on the northern coast.
Bouchart, who has often clashed with the government over the camp, claims it could soon contain as many as 15,000 migrants if authorities take several months to dismantle it.
Calais residents are due to stage a protest on Monday over the effect the presence of thousands of migrants has had on their livelihoods.
"I am in Calais today fully aware of the serious difficulties you face each day," Cazeneuve said Friday.
Crowding at the camp is causing fresh tensions.
Two migrants were seriously hurt on Tuesday in what appears to have been a fight between Sudanese and Afghan residents.
The Jungle's population also includes large numbers of Somalis, Kurds and Syrians.
Cazeneuve has announced that 200 more armed police will be deployed to the site to prevent near-daily attempts to stow away on lorries heading for the ferry port, bringing the total number of police in Calais to 2,100.
Since last October, more than 5,500 asylum seekers have left Calais for 161 special accommodation centres set up around France.
Political hot potato
Franck Esnee, head of the Medecins Sans Frontieres (Doctors Without Borders) branch working at the camp, agreed that the Jungle should be dismantled but said the proposed alternatives were "insufficient".
Additional permanent accommodation is needed, he said, adding: "The government needs to encourage initiatives by local mayors who are proposing to take in migrants in their towns."
The government should also encourage the requisitioning of public buildings to house migrants, he said.
Cazeneuve told the regional paper Nord-Littoral that accommodation for thousands of migrants would be created elsewhere in France in an attempt "to unblock Calais".
The fate of the camp is already featuring prominently in campaigns for next year's presidential election.
Former president Nicolas Sarkozy has called for Britain -- the country the migrants want to reach -- to take responsibility for migrants wanting to cross the Channel.
"The English should examine the requests of all those who want to go to England and they should do it in England," he told a rally last Saturday in the nearby coastal resort of Le Touquet.
Meanwhile the British government has dismissed as a "complete non-starter" a proposal by Xavier Bertrand, the president of the region including Calais, to allow migrants to lodge British asylum claims on French soil.
After Cazeneuve met British counterpart Amber Rudd in Paris on Tuesday, the ministers presented a united front.
"We are committed to working together to strengthen the security of our shared border (and) to strongly diminish the migratory pressure in Calais," they said in a joint statement.
