The Washington Post first reported on the aborted landing at Andrews Air Force Base due to an air traffic controller allowing the two aircraft to come too close.
Obama was aboard a Boeing 737, one of the fleet of presidential passenger jets, returning from an appearance on ABC's "The View" in New York, when the near-collision happened on final approach to Andrews.
The Obama plane aborted the landing because it "did not have the required amount of separation behind a military C-17," the Federal Aviation Administration said in a written statement. "The FAA is investigating the incident. The Boeing 737 landed safely after executing the go around. The aircraft were never in any danger."
The FAA's statement didn't address the role of air traffic controllers in the mishap.
The incident is the latest embarrassment for the FAA, which is dealing with the fallout over several air traffic controllers falling asleep this year, some while planes tried to land.
Monday's mishap didn't involve a sleeping air traffic controller. Instead, the civilian controller at the Warrenton radar control center allowed the Obama plane to get too close to an Air Force C-17 plane in front of it, the Post reported.
The FAA requires a separation of five miles between planes at that lower altitude because the turbulence off of the wings can be dangerous to following planes.
The civilian controller in Warrenton reportedly told the military's controller at Andrews that the distance between the planes was four miles -- an estimate that turned out to be inaccurate. The distance was just over three miles.
The controllers at Andrews ordered the Obama plane to execute a series of "S-turns" in an effort to increase the distance but that was ineffective. The military controllers weren't sure there was enough time for the C-17 to get off the runaway once it landed for the first lady's plane to land on the same runway. So they instructed the Obama plane to abort its landing.
Michelle Obama's office said it would not be commenting on the incident.
An Andrews Air Force Base spokesman would say only that Obama's plane was asked to circle the runway to allow the C-17 time to clear.
Fox News' Doug McKelway contributed to this report.