The White House said the incident happened on Monday as the first lady was returning from her appearance on "The View" on Executive One Foxtrot.
The FAA said in a statement that the plane did not have the required amount of separation behind a 200-ton military cargo jet as it should have when it was approaching the base, so it was instructed to perform a "go around" just after 5 p.m.
FAA officials told ABC News that the first lady's aircraft was three miles away from the military jet, whereas the standard distance is five miles.
The problem apparently arose when the air traffic controller at radar control center in the D.C. area handed off responsibility for the two planes despite the fact they were too close together.
"If an airplane is too close behind another airplane, the small tornados that come off the airplane in front can actually upset the airplane flying behind, and cause the airplane flying behind to lose control," said Steve Ganyard, a former Marine fighter pilot.
According to the Washington Post, military controllers realized the problem and asked Mrs. Obama's pilot to perform a series of maneuvers to put more space between the two planes. When that didn't work they told the first lady's plane to make another pass before landing safely.
Authorities said the incident did not cause any panic, and the first lady's plane was never in any danger.
A government source said nobody aboard the plane was aware of anything out of the ordinary. The government source also said an emergency was not declared, and emergency vehicles did not respond.
However, the incident comes at a time when air traffic controllers are already under scrutiny for several reports of air traffic controllers falling asleep on the job. An air traffic controller was suspended on Tuesday after being caught watching a movie on a DVD player while on the job.
The FAA is investigating the latest incident as a possible error by controllers.