The lucky passengers were treated with a stunning bird's-eye view of the Matterhorn, Zermatt, Aletch Gletcher, Eiger and Jungfrau.
A passenger on board, Lars Jensen, said the experience was "absolutely spectacular" in a Facebook post to Swiss International Airlines.
"I will fly with you again next time," he added.
A spokesman for Swiss Airlines confirmed that air traffic control had approved the impromptu tour.
"Pilots are permitted to fly different holding patterns (for example over the Alps instead of over the central plateau) if authorised by air traffic control," a spokesman for Swiss Air Lines told swissinfo.ch.
"Safety is always our first priority. However, holding patterns over the Alps do not differ from holding patterns elsewhere in terms of safety or concerning arrival time."