The soldiers from Joint Task Force East will set up modular tents equipped with lighting and heating on a privately owned site leased by the government in Saint-Bernard-de-Lacolle.
Canada has sent about 100 soldiers to a remote spot on the Quebec-New York border where asylum seekers are crossing illegally. The residence will be able to house roughly 300 people.
Hundreds of Haitians have crossed into Quebec in recent weeks, spurred partly by false accounts of asylum seekers being able to immediately obtain residency after entering Canada.
The migrants fear the U.S.is becoming less welcoming and have made a decision to try their luck seeking asylum in Canada.
According to an estimate by the union representing Canadian customs workers, between 450 and 700 people are crossing the border every week.
The military would have no role in security matters, Le Bouthillier said in emailed statement. All but a few will return to their home base once the site is completed.
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Montreal's Olympic Stadium is being used to as a shelter in August, and the city also plans to use the decommissioned Royal Victoria Hospital into a 320-bed facility.
In May, U.S. President Donald Trump announced that he would not be extending temporary protection status for Haitian nationals past January, when it's set to expire.
Rodrigue said the visit was to show asylum seekers "the Haitian people and government are with them, are behind them and don't forget about them".
Earlier in the day, in nearby Hemmingford, some 40 asylum seekers sat under white tents at an impromptu reception centre that has sprung up on the Canadian side of a popular illegal border crossing.
Numerous recent refugee claimants crossing into Quebec are Haitians who have been living in America for years but now face deportation.