Yes, an individual person can be an MSB. An individual conducting a business that is not formed as a partnership, LLC, corporation, etc. is a sole proprietor. If you look at the definition of an MSB and the FINCEN related definition of "person", you will see:
Person - A "person" is an individual, a corporation, a partnership, a trust or estate, a joint stock company, an association, a syndicate, joint venture, or other unincorporated organization or group, an Indian Tribe (as that term is defined in the Indian Gaming Regulatory Act), and all entities cognizable as legal personalities.