Is a professor allowed to require me to give him permission to speak with my doctor before letting me make up an exam? I study in the USA.

Can a professor ask me to waive my right to privacy so he can talk to my doctor about my medical condition? He says he needs that in order to allow me to take a make-up midterm for an exam that I missed, even though a medical note certifying my illness is provided.

Also, the doctor that gave the note is usually a nurse practitioner (NP), but he instead wants a note from a doctor of medicine (MD).
That sounds like a big no to me, but that comes from Germany with very strict rules on privacy. Your medical condition is your thing, and yours alone. If you have a document that certifies your illnesss, that should be enough.

Check your university policies, what you need to provide in case off illness HAS to be written down somewhere. If it states there that a written thing is enough, it is enough. Point your professor to that document, if that does not help talk to faculty cousellors. They should be able to help you.