No, you can't do that. At least not by just clicking a button and setting a password.
It might be possible using macros and password protecting the macro editing function, but that is a much more complicated process which may prevent other parts of the document from working correctly if they need to include macro functions.
You should also be aware that there are many programs available on the Internet that will bypass all protection in a Word document and allow it to be saved so that it can be altered or edited by anyone.
So basically you cannot protect Word documents or any part of a Word document if someone has a copy of the password unlocking software. I have used it to open locked documents where someone has left an organisation and failed to leave the access password. It is 100% effective at gaining access in a couple of seconds.