I have a arduino pro micro that runs on 5v. I also have a Max4466 that needs 3.3v, however the pro micro doesn't seem to have a 3.3v VCC. Is there any way to attach the max4466 to the Board?
You need to add an external 3.3V voltage regulator. You can get these quite cheap on eBay (etc) as a module - some even come in a breadboard friendly format.
Power it from the 5V from the Arduino, then power your MAX4466.
However, the MAX4466 can run at up to 5.5V, so I fail to see why you think you need 3.3V.