The unidentified man was taken into custody and explosive disposal teams were on the scene, Secret Service spokeswoman Cathy Milhoan told reporters in the White House briefing room.
The package was being inspected, she said.
"We separated the individual and the package. He is now in Secret Service custody," she said.
"We established a security perimeter, so the media was moved in here and East Wing tours were temporarily suspended. All other activity in the White House continues as normal."