First lady Melania Trump took a seat, July 13, during a visit to The Royal Hospital Chelsea in central London.
Pool reporters said a "thin haze of smoke" was visible and smelled something burning.
The airplane returned to Joint Base Andrews, an air force facility used by the White House outside Washington DC.
She was on her way from Washington to Philadelphia when there was "a minor mechanical issue", according to her spokesperson Stephanie Grisham.
A flight crew member gave passengers damp towels to hold over their faces for the smell, the reporter said.
"Smell and smoke have since dissipated", NBC's Peter Alexander tweeted.
The plane landed back at the base and Ms Trump was awaiting a new aircraft to travel to Philadelphia where she was visiting families of children who were affected by exposure to opioids while in the womb.
One of the components of the first lady's "Be Best" initiative is helping children dealing with the opioid crisis.
U.S. Health and Human Services Secretary Alex Azar will reportedly accompany Trump on her visit, during which she will tour a neonatal intensive care nursery.