See title. I can't explain anything on this, but I have to mention that this question is about businesses within the U.S.
It depends on what the FBI is ordering the business to do, and on why and how the order is made. If the FBI orders the business to commit a crime, then then the business is not only not obligated to carry out the order, but it is obligated not to carry out the order. It is of course unlikely for the FBI to order anyone to break the law, but there are surely areas where the law is unclear or disputed where this might happen. An example might be ordering the disclosure of information contrary to a law protecting the information from disclosure. Any dispute about such an order would ultimately be resolved by a court.
If the FBI orders the business to do something legal, but the order doesn't have a lawful basis, then the business is not obligated to comply. The FBI and the business are likely to disagree about whether the order is lawful, of course, and this disagreement would similarly be for a court to resolve. It is not sufficient for an officer of the business simply to assert to an FBI agent that the order has no lawful basis.
If the order does have a lawful basis, then yes, the business must comply.
I assume the question is about being "legally" obligated, since we don't have an emperor. The FBI itself doesn't command, but an individual agent can command claiming legal authority. A janitor working at the FBI does not have any special legal authority. An FBI agent has powers of search and seizure, but those powers are circumscribed by law: an agent's can't unilaterally decide that you must be a crook and demand that you let him in to your home to conduct a search. The agent might have a warrant, or probable cause. So in some (narrow) cases, you are required to obey. Most "orders" are court orders, carried out by the FBI. However, if agents are investigating a crime scene, you might be interfering with the investigation and they could legally order you to get back behind the yellow line. It really depends on the order, and why they give it. It's hard to imagine what "order" the FBI would give to a business. Most likely, the court has issued a search warrant, which the FBI is executing. You have to obey the court, and allow the FBI to search.