University Street remains closed in both directions between Notre-Dame Street and Saint Antoine Street.
The incident took place Friday morning around 2:20 a.m. ET.
Const. Anie Lemieux says a vehicle was going south on University when the driver lost control and hit an oncoming taxi.
There were five people in the taxi.
One woman was taken to the hospital with minor injuries. The other people in the car did not require medical treatment.
Police are still looking for the driver who left the scene before officers got there.