Calculus, per se, isn't a requirement, but physics is covered pretty heavily on the MCAT. And last I checked, you needed calculus for college level physics.
To my utter shock - I thought it'd be one of the last bulwarks against premed memorization. When I learned otherwise, it was sad to think that those students who flocked to non-calc physics (and floundered; the classes are of course curved) really would have a good shot at medical school.
Most universities have a physics sequence that does not require physics. A major reason this sequence exists, at least at the university that employs me, is pre-med students. Also, physics is not "covered heavily" on the MCAT.