Depends on the school. The school I got my MPH from didn't require any exam, but I believe that most require the GRE. I doubt that any require the MCAT as you don't have to qualify for med school to do an MPH.
What are you wanting to do your MPH in? Mine is in health admin and policy.
for most MPH programs, you have to take the GRE. it shouldn't take too much preparation though. i would suggest something simple like the princeton review software available at most stores. it goes over all the covered material and even has practice tests that are fashioned after the actual, computerized exam. nothing to stress about really, especially if you're comparing it to the MCAT at least.