There are no specific restrictions that I am aware of. This is particularly the case for the Reserves and National Guard (though the National Guard is run by the State - so there may be some additional considerations depending upon the state), as most people have other jobs outside the military and some have their own businesses.
Depending upon what type of business you do, and your customer/client base, there may be some security clearance concerns - but aside from that, nothing says you can't be an active duty service member and own a business, even while deployed. You can't (or shouldn't) use your military affiliation to advertise for or 'authenticate' your business, but you can run a business as a military member.