The rule is written into American Airlines' conditions of carriage, right next to other undesirable behaviours such as being under the influence of drugs or alcohol, being armed with a dangerous weapon, and being violent or abusive.
A number of other, mostly American airlines have the same rule, including Delta Air Lines, JetBlue, Spirit Airlines, Alaska Airlines and Hawaiian Airlines. Puerto Rico's Seaborne Airlines has a similar clause.
Some Asia-based airlines including Bangkok Airways and Air Asia stipulate that passengers carrying notoriously foul-smelling fruit, such as the infamous durian, on-board can be banned from doing so.
Spanish airline Vueling will refuse to carry your pet if it has an "unpleasant smell".
In Australia, Qantas and Jetstar don't specifically mention body odour in their conditions of carriage but Virgin Australia says it can refuse carriage of baggage "because of any odour it emits".
None of these conditions spell out exactly how much a person - or their fruit, pets or carry-on bags - has to stink to justify being rejected from the aircraft.
But if you think an airline has never enforced this little-known rule, think again.
American Airlines removed a French man from a 2014 flight from Paris to Dallas after several passengers complained about his body odour.
In 2010, Air Canada famously kicked a passenger off its flight from Charlottetown to Montreal for emitting what fellow passengers described as a "brutal" odour.
Passengers reportedly complained to staff, who asked the man to leave the plane, delaying the flight for about 20 minutes.
"As an airline, the safety and comfort of our passengers and crew are our top priorities," an Air Canada spokeswoman told America's ABC News at the time of the incident.
"Therefore, any situation that compromises either their safety or comfort is taken seriously and in such circumstances the crew will act in the best interest of the majority of our passengers."
But smell is subjective, so how much does a person have to stink before they're deemed to be not airworthy?
"Everyone has their own threshold," an American Airline spokesman previously told the LA Times.
"We try to resolve the situation with respect (for all parties)."
A Northwest airlines spokeswoman said: "It's handled on a case-by-case basis."