The aircraft carrying her was too close to a 200-ton military cargo jet and had to scrap its final approach to Andrews Air Force Base, a key hub for top US government officials including President Barack Obama, the reports said.
"The aircraft were never in any danger," the Federal Aviation Administration (FAA) said in a statement that confirmed an incident at Andrews but did not explicitly say the first lady was aboard the aircraft directed to veer off.
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The Washington Post and ABC television each cited anonymous federal officials familiar with the events. CNN meanwhile reported that Jill Biden, wife of Vice President Joe Biden, also was on the aircraft.
Controllers at Andrews worried that, as a result of other air traffic officials' mistake, the massive C-17 would not clear the runway at the facility swiftly enough for the first lady's Boeing 737 to land safely.
The Andrews controllers ordered Michelle Obama's flight -- bearing the EXEC1F designation as an aircraft carrying members of the president's family -- to execute a series of turns to put more distance between it and the cargo.
"FAA controllers at Andrews Air Force Base instructed an incoming Boeing 737 on approach to Runway 19 to perform a 'go around' on Monday, April 18, 2011 just after 5 pm because the plane did not have the required amount of separation behind a military C17," the FAA said in its statement.
"The FAA is investigating the incident. The Boeing 737 landed safely after executing the go around," the agency said, without mentioning Michelle Obama.
The FAA has strict standards on how much distance controllers must maintain between planes, because an aircraft's wake causes severe turbulence.
The FAA requires five miles (eight kilometers) between a C-17 and the next airplane, but the first lady's jet was just 3.08 miles (4.8 kilometers) miles away, the Post said.
US air traffic controllers have faced heavy scrutiny recently after a series of incidents in which some fell asleep while on duty, leading officials to announce a new "zero tolerance" approach for such activities.
Transportation officials monitoring some of the world's busiest air traffic have been red-faced as case after case of workers snoozing in US airport towers came to light in recent weeks, in some incidents leaving pilots of passenger jets to land unassisted in Washington.
The head of US air traffic control resigned last week and the FAA vowed a major shake-up to win back public trust in its safety.
"We expect controllers to come to work rested and ready to work and take personal responsibility for safety in the control towers," Secretary of Transportation Ray LaHood in a statement announcing the new rules.
"We have zero tolerance for sleeping on the job," he said. "Safety is our top priority and we will continue to make whatever changes are necessary."
