The minister, Gerard Collomb, visited the port city on Friday and earlier said extra police would be drafted into the area.
French authorities sent in bulldozers last year to clear a migrant camp known as the Jungle, where thousands of migrants hoping to cross the Channel to Britain lived in squalid conditions. Many of them were sent to lodgings around France.
Collomb took a firm line during a visit, saying a new center would recreate the situation that existed before the Jungle camp, considered a public health risk, was demolished.
"We don't want to create a gathering point where numbers would swell back up to 7,000 over time. That would not be tolerable, for the migrants, the residents of Calais and for economic life," he told reporters on arrival.
Aid agencies say about 400-600 migrants are once again gathered and sleeping rough on streets.
Before it was demolished, the Jungle camp had become a symbol of Europe's difficulty in dealing with the migrant crisis. Charities had warned the Socialist government at the time that migrants would return.
Newly elected President Emmanuel Macron and his centrist government have come under pressure from the human rights watchdog which has described conditions facing migrants in Calais as "inhuman".
"Refugees make up 0.25 percent of Europe's population. Can we really not look after them ?" Jacques Toubon, head of the national human rights watchdog, said on RTL radio.
"These people are equal in dignity, equal in their rights ... and France's legal obligation is to accord them basic human rights."
Macron has instructed local officials to treat migrants more humanely, government spokesman Christophe Castaner said, and he has also asked Collomb to see to it that asylum requests are processed within six months.
Collomb told the regional Nord Littoral newspaper that he was sending additional mobile police units to the Calais area.
Earlier this month, two French charities accused police of using excessive force against migrants and preventing aid groups from distributing meals.
Many migrants set on crossing the short stretch of sea from Calais to Britain, try to do so by slipping inside the cargo holds of large trucks bound for English shores.