An interior pane of ballistic glass stopped the round.
Authorities are investigating whether the bullet is related to a reported shooting between two vehicles on Constitution Avenue about a half-mile from the White House on Friday.
An AK-47 assault rifle was found in one of the vehicles, which had been abandoned. An arrest warrant has been issued for 21-year-old Idaho resident Oscar Ramiro Ortega in connection with the incident.
Ortega is facing felony charges of carrying a dangerous weapon. President Obama and the First Lady were not at home at the time of the shooting.