Mr Clinton was on a flight to Los Angeles to attend a party fundraising event when the pilot was forced to rise quickly.
White House spokesman Joe Lockhart said the presidential plane was descending to 10,000ft as a commuter plane heading in the opposite direction was ascending to 9,000ft.
He said the automatic collision avoidance installed in Air Force One warned the pilot to climb to avoid the danger.
The pilot took Air Force One to 10,400ft and banked away from the commuter plane.
Mr Lockhart said the two planes did not come closer than 1,000ft - the minimum vertical separation required by federal air safety regulations.
"This was not a near miss by any calculation. At all times they maintained the required separation," he said.
Journalists on board the plane said it suddenly rose sharply, pushing passengers forcefully into their seats.
One of the media party, Joyce Naltchayan, a photographer for the French AFP agency, described the ascent as "very dramatic".
Ms Naltchayan, who was standing up at the time, was knocked back into her seat.
Mr Clinton was travelling form Palo Alto, California, to Los Angeles International Airport. Air Force One touched down safely at 1902 local time (0302GMT).
Previous concern
In March, the president was on board Air Force One when the plane disappeared briefly from an air traffic controller's radar screen.
The plane, on a flight from Andrews Air Force Base outside Washington to Hartford, Connecticut, stayed in constant radio contact well away from any other aircraft.
The apparent disappearance was recorded by radar equipment at Gibbsboro, New Jersey, which was taken out of service to investigate the malfunction.
The president's air fleet is made up of two planes - both converted Boeing 747s - and whichever one Mr Clinton is on adopts the Air Force One call sign.
Each plane has a executive suite with presidential office and separate accommodation for guests and media travelling with the president.
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