This is a complex question. Military police are law enforcement officers employed by the Federal government. So technically, they are Federal Law Enforcement Officers. I think the information you may be looking for is what are military police authorized, or not authorized to do in that capacity.
Military police officers typically do not have the legal authority to conduct law enforcement activities outside of the jurisdiction of a military base. The legal basis for this is the Posse Comitatus Act of 1878 (18 U.S.C. § 1385). This Federal law prohibits military personnel from engaging in law enforcement activities. There are many exceptions to this prohibition, though. Some of the exceptions include: law enforcement activities of the Coast Guard, law enforcement activities on military property, law enforcement with respect to national security sites (e.g., nuclear weapons), at the request of the President, and some others.
There may be other State or Federal laws and regulations that specify applicability to “Federal Law Enforcement Officers.” Whether or not these apply to military police officers depends on how the term is defined in those specific laws and regulations.