The first lady landed safely back at the base at around 9am local time (2pm BST).
The aircraft was leaving from Joint Base Andrews in Maryland bound for Philadelphia on Wednesday morning (local time) when a thin haze of smoke was visible in the cabin, U.S. media reports.
Within a few minutes the smoke and burning smell began to dissipate, according to the producer. Secret Service agents rushed to the front of the plane, and press were handed wet towels to hold over their faces in case the smell was too strong.
CNN said the White House did not immediately comment on what had happened. A spokeswoman said the first lady was "fine" after the "minor mechanical issue" aboard her plane.More news: Celebs, Fans Blast Piers Morgan For Dad-Shaming Daniel Craig
Mrs Trump was travelling to a hospital in Philadelphia, Pennsylvania to meet with families of children who were affected by exposure to opioids while in the womb when the incident occurred.
Mrs. Trump was to tour a neonatal intensive care nursery and speak at an HHS conference on a new system that tracks infants suffering from opiate withdrawal.
The First Lady's visit is part of her "Be Best" campaign, which focuses on major issues affecting children.