I am installing a new Harbor Breeze ceiling fan. When I removed the old fan a small bracket was drilled into the ceiling attached to a beam in the ceiling. There was no actual outlet bax in the ceiling for the mounting bracket. How would I attach a outlet box for the mounting bracket or is there another way? Do I need to cut into the drywall in the ceiling to attach an outlet box? Thanks.

Yes. Cut sheetrock hole the size of pancake box. Use a fan-rated "pancake box" and screw it securely to the beam with the screws that come with the box.