The smell was reportedly coming from "a malfunctioning comms unit" on board.
"Smell and smoke have since dissipated", NBC's Peter Alexander tweeted.
It was not immediately clear what caused the problem on the aircraft, a Boeing C-32A identified as "Bright Star".
The First Lady was traveling to Philadelphia to visit families of children affected by exposure to opioids in the womb and a neonatal intensive care nursery. Reports show that smoke and burning smells became overwhelming, forcing members of the press pool to hold wet towels over their faces.
She could be seen safely walking off the plane after the flight returned to Joint Base Andrews in Maryland.
Stephanie Grisham, the first lady's communications director, told CNN the incident was a "minor mechanical issue". She said the team is "evaluating" whether to make other arrangements to travel to Philadelphia.
The trip remains on for later Wednesday and the first lady will take a different plane, Grisham said.
She was joined on her visit to Thomas Jefferson University Hospital by Health and Human Services Secretary Alex Azar.