Montreal police Const. Yannick Ouimet said the crash happened at 4:35 a.m. near the intersection of de l'Esplanade Avenue.
The driver was travelling east at high speed when he lost control of the car. The car rolled and took out a lamppost and a tree before coming to rest on the terrasse. A man in his 20s and a female passenger, also in her 20s, were found in the vehicle by emergency workers.
They were taken to hospital with serious but non-life threatening injuries.
Police say speed and alcohol may have contributed to the crash.
Mont Royal Boulevard will remain closed until mid-day as police investigate, and the debris is cleaned up.