Police say the man was detained near the Naval Observatory and that a long gun, ammunition and several handguns were found in his car that was parked in a DC garage.
Ms Harris and second gentleman Doug Emhoff are staying at Blair House until the historic building is ready for them to move in.
The arrest of Paul Murray, of San Antonio, Texas, came after police in his homes state tipped-off DC authorities, according to reports.
Murray, 31, was was charged with carrying a dangerous weapon, carrying a rifle or shotgun outside of a business, possession of unregistered ammunition, and possession of a large capacity ammunition feeding device.
The US Capitol Police confirmed an alert for a suspect went out to various agencies in the DC area Wednesday afternoon but they have not confirmed what the nature of the intelligence received was.