Does a master's in a non-medical field hurt medical school admission chances?

Not necessarily. Some people major in history and go to medical school. You just need certain prerequisites. Such as organic chem, calculus, bio etc. You can get those classes in even if you had a different major. Medical schools like Harvard per say would prefer a bio major. If you have the required classes then you are fine. However, you are also going to need some clinical research, or some hospital interning on your side. Medical schools are very selective and even those schools who are nor ivy leagues are very selective.