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President Barack Obama and Vice President Joe Biden were at work at the time and they were "relocated" immediately, he told reporters at his daily press briefing after the incident.
Gibbs declined to say where the president was moved to, and said he had no information on whether First Lady Michelle Obama was also relocated.
He said the president was moved out of an "abundance of caution."
"It was a very brief period," Gibbs added.
Not long after the incident, Obama appeared at a White House event promoting his plans to make college more affordable.
Security officials at the White House and the Capitol were put on alert during the incident and cleared tourists and others from outside areas around the two buildings. The alert was canceled a short time after it was issued.
Authorities also took steps to evacuate the Capitol.
The Senate was in session, and briefly recessed.
The House was not meeting at the time.
After the Cessna 180 small plane flew into the restricted airspace, the pilot complied with directions to leave the area, according to the Department of Homeland Security.
Military jets took off to intercept the single-engine plane, she said.
"The episode was over within minutes as two F-16 fighter jets and two Coast Guard helicopters were dispatched and intercepted the plane," said U.S. Northern Command spokesman Michael Kucharek.
The pilot was then directed to land and the plane touched down at an airport in Indian Head, Maryland, in the Washington suburbs.
According to sources in the White House, at around 12:40 p.m. local time (1640 GMT), Secret Service officers began ordering camera people, correspondents, and anyone else on the White House driveway into the press building.
Ten minutes later, the "all clear" was given and everything goes on as usual.