We understand that it is the doctors recommendation for Josh to wear a protective face mask. Should word Doctor have and apostrophe in this sentence?

Yes, the word "doctor's" should have an apostrophe in this sentence.

The apostrophe is used to indicate that something belongs to someone or something else. In this case, the face mask belongs to the doctor. Therefore, the correct way to write the sentence is:

"We understand that it is the doctor's recommendation for Josh to wear a protective face mask."