Around 250 asylum seekers are arriving each day in Montreal, the largest city in Canada's mainly French-speaking Quebec province.
Officials estimate that 400 people crossed the border at the site on Sunday alone.
"The Canadian Armed Forces are aware of the hard situation that is requiring significant resources of Canada Border Services Agency, the Royal Canadian Mounted Police and other partners in the area of St-Bernard-de-Lacolle", the military said in a statement.
The soldiers will have no role in security matters and will not participate in law-enforcement tasks.
Francine Dupuis, of Praida, a provincial programme for the reception and integration of asylum seekers, told the BBC that another 1,200 people crossed into the province in July, about 90% of them from Haiti.
Canada said last week it planned to house some migrants in Montreal's Olympic Stadium.
The Canadian immigration ministry, on its Facebook page on August 5, discouraged illegal entries and noted that messages posted elsewhere online suggesting that Canada is inviting people to seek refugee status were wrong.More news: British Columbia opposition leader resigns after fall from power
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"There's the United States; this is Canada".
"Of this number, a little more than 700 people are staying in the Olympic stadium waiting for access to permanent lodging", she said.
The camp is being built in anticipation of a large influx of asylum seekers from the USA, said Stéphane Malépart, a spokesperson for Canada Border Services Agency (CBSA).
The same could happen in Canada if an asylum seeker's claim is rejected.
In the United States, the Trump administration is considering ending a program that granted Haitians so-called "temporary protected status" following the massive quake that struck Haiti in 2010.
The administration of U.S. President Donald Trump has taken a tougher stance on immigration with plans to cut legal immigration by 50 percent over 10 years.