Halton Regional Police and other emergency responders were called to the intersection of Dundas Street and Eighth Line just after 8:30 p.m. on Saturday.
Police say the crash occurred as the SUV was making a left turn onto Eighth Line.
The motorcycle driver was rushed to hospital in Hamilton. The 23-year-old man suffered life-threatening injuries and police said Sunday that he remains in critical condition.
A person who had been riding in the back of the SUV suffered serious injuries in the same crash, but is expected to recover.The SUV driver and the other passengers in the same vehicle were not seriously hurt, police say.
An investigation into the collision continues. Police say alcohol does not appear to be a factor.
Any witnesses are asked to contact investigators at 905-825-4747 ext. 5065.