They say the 60-year-old driver was stopped by police at the scene of the collision with a 93-year-old pedestrian.
However, police say because she spoke neither French nor English, and did not realize that she was required to stay with police.
The woman struck the man while he was crossing the street yesterday at around 6:20 a.m. on Barclay Avenue near the corner of Légaré Street.
Police say he remains in critical condition, though his life is no longer in immediate danger.
Officers spent Monday morning trying to track the woman down, thinking she fled the scene on purpose.
For now, she faces fines related to not giving pedestrians the right of way.
Police say further charges could be laid in coming days, however, she will not be charged for hit-and-run.