I bought a new bike and when I put it on my bike rack in my garage the arm of the rack sits on the rear brake cable, putting some tension on the cable. Could this cause brake problems and if so what can I do to mitigate this?
Could this cause me to have brake problems
Yes: The weight of your bike will pinch the cable and slowly cause the cable to lose its structural integrity and become damaged: They are designed to take stress along them (tensile strength), not laterally (shear strength)... hence how they can withstand huge amounts of force from braking yet can easily be cut with cable cutters by most healthy people.
what can I do to mitigate this?
Don't pinch the brake/shifter cables between anything. If your rack pinches them, adjust the rack or get a new one.