Do I have to have an engineering bachelors for graduate school?

I was wondering if it is necessary to do a Bachelors in Engineering as well as a Masters in Engineering.

I am currently enrolled in University of Toronto Scarborough Campus in Bachelors of Science, and I am planning on doing a double major of Biochemistry, and Physics & Astrophysics.

However I feel as though most Masters of Engineering Programs require a Bachelors of Engineering.
So do I have a chance at going to Engineering school after this, or should I just switch unis to somewhere that I can do a degree in Chemical Engineering.

My uni does not offer any engineering btw, not my campus anyway.

I am only in first year right now so switching unis is really not going to be a big deal hopefully.
posted by interestedinchemeng, Toronto on March 25, 2014