A vehicle trailed behind the Obama daughters’ motorcade as car barriers were lowered on Pennsylvania Avenue.
The driver was arrested and city police checked the car for explosives.
The US Secret Service told the BBC the driver was an employee of the US Department of Treasury, but did not necessarily work at that location.
The driver, Mathew Evan Goldstein, 55, was charged with unlawful entry.
A spokesman for the presidential security force would not confirm whether the incident was a result of a wrong turn or malicious intent.
The lockdown, which began shortly after 16:40 local time (21:40 BST) lasted about half an hour.