In a statement, police said the food inspection agents were granted a warrant to search the farm’s property.
RCMP officers were requested to accompany them, they said, due to “increased tensions” and “protests” on the farm.
Katie Pastiney, one of the owners of Universal Ostrich Farms in Edgewood, British Columbia, said in a Facebook post on Tuesday that she and her mother Karen Espersen were arrested while trying to feed the ostriches.
Ms Pastiney and Ms Espersen have vehemently opposed the cull order on the ostriches, and had launched a months-long court battle in a bid to stop it.
That battle has attracted international attention, including from US Health Secretary Robert F Kennedy, who penned a letter in May to the head of the CFIA asking the agency to study the birds instead.
Dr Mehmet Oz, the administrator for the US Centers for Medicare and Medicaid Services, offered separately to re-home the birds on his Florida ranch, Ms Pastiney told CBC News in May, though the farm rejected the offer.
She had previously urged US President Donald Trump and billionaire Elon Musk, who has Canadian citizenship, to intervene.
The CFIA ordered that the birds be culled in December after an avian flu outbreak on the farm killed 69 ostriches.
“Allowing a domestic poultry flock known to be exposed to avian influenza to remain alive allows a potential source of the virus to persist,” the CFIA had said.
“It would increase the possibility of reassortment or mutation, particularly with birds raised in open pasture where there is ongoing exposure to wildlife. This could also increase the human health risk.”
Video posted by Ms Pastiney on Facebook on Tuesday shows CFIA officials building enclosures on the farm using hay bales, which she said were being used “to chase our ostriches into square corrals”.
Local media reported that part of the hay-bale wall caught fire early on Wednesday morning, and firefighters were seen hosing down the flames. It is unclear what caused the fire.
Protestors have been gathered at the farm since Monday, following the arrival of the RCMP and CFIA officials.
The Supreme Court’s intervention comes after a Federal Court of Appeal judge ruled on 12 September that the cull can go ahead.
Judge Gerald Heckman said in his ruling that the farm has failed to establish any “serious or arguable issue” for why its case should be heard by the highest court.
In Wednesday’s order, Supreme Court Justice Michelle O’Bonsawin said the CFIA must maintain custody of the birds and the farm must not interfere while it decides on whether to hear the case.
The federal inspection agency must respond to the appeal by 3 October, Justice O’Bonsawin ordered.
The BBC has reached out to the CFIA for comment.