No, you are not required to take any courses to take the exam, but you will have a hard time completing the test with a sufficient score without taking your medical school prerequisite courses first.
The content on the MCAT is covered by introductory courses at most colleges and universities. You should reach out to your pre-health advisor, who can help you determine the best way to fulfill the prerequisite courses for your selected medical schools. Generally, course requirements will be pretty similar, but variations do occur.