A spokesman for the city's ambulance service said he's never seen anything like it in his 30-year career.
"We see accidents in escalators, but I don't recall a situation like this where somebody was physically trapped in the mechanism," said Bob Lamle, a division chief for Urgences-sante.
The ambulance service has received several calls about people falling in the subway, he noted.
Police say the victim was a 48-year-old woman. Earlier reports said she was 47.
Firefighters were first on the scene, followed by paramedics.
"By the time our people arrived, it had stopped and she was at the bottom of the escalator," Lamle told reporters outside the Fabre subway station in the city's north end.
"What they found was a woman. . . who was clearly trapped," he said. "She was lying on her back."
He said firefighters and paramedics immediately tried to revive her but were unsuccessful. A doctor then declared her dead on the scene.
The accident happened at around 9:15 a.m., during the morning rush hour.
"There were people who saw this and tried to help," Lamle said.
A Montreal police spokesman said the woman was travelling down the escalator toward the subway platform when her scarf was trapped.
"She took the escalator to descend toward the metro (subway train) and, at a certain point, her scarf got caught in the mobile escalator," Jean-Pierre Brabant said.
"She was going down the escalator, her scarf remained stuck, and she tried to pull on the scarf to try to get it out and her hair also got stuck."
There were media reports the woman was wearing a hijab, but that was denied by Brabant.
"A lot of people are talking about a hijab, (but) the information that I have is that it's a scarf that got caught."
Brabant said investigators will review videos from cameras inside the subway station to find out more.
This is not the first tragic accident in the Montreal subway system in the past year.
In April 2013, a young woman died because she may have been distracted by her cellphone.
Video footage from the subway showed the 20-year-old woman wearing earphones and staring into her smartphone before she stepped into a gap between two cars.
She was dragged for two stops before commuters noticed blood on the tracks.