A 2003 statute specifically protects "any structure, plaque, statue, or other monument on public property commemorating the service of any person or persons in the armed forces of the United States."
President Trump cited that law, first in a Tweet and then a few days later in an Executive Order which also referred to multiple other laws and provisions protecting federal property from what it termed "senseless destruction." As for monuments and memorials on state or local government property or in private hands, the order says that state and local law-enforcement agencies failing to protect such property will be "subject to the withholding of federal support."