Ravinder Kaur Arora, who is set to be deported to Delhi on Sunday with her family, had a seizure and was taken to a Montreal hospital.
The family had its claim for refugee status rejected by Canadian authorities. They were to board a flight from the Trudeau airport at 11 p.m. ET.
Arora has a condition known as intractable epilepsy. Her seizures could lead to serious health complications and death.
In a plea to Qatar Airways, the company set to transport Arora and her family to Delhi, her doctors asked that her deportation be delayed because she requires surgery.
"My mother is very sick," said Tarandeep Arora, the woman's daughter.
"She needs to stay until she can undergo surgery later this month. My father needs to be here to take care of her as well as my younger sister and brother.
"After 16 years of living with her, he knows what to do when she has seizures," she added.
Arora's husband, Amrit Pal Singh Arora, was brought to the Immigration Prevention Centre in Laval on June 28.
The family has been residing in Montreal for six years.