American media is reporting on small aircraft and American management.
No one was hurt.
Danish police confirmed that the incident took place on Monday night, though they did not mention Pink by name.
Danish media reported Pink, who performed in Oslo on Monday evening, was not on the flight.
Police said that private Cessna plane with 10 people on board caught fire on landing at the Aarhus airport.
It said the plane had flown from Oslo and that on board included seven passengers: four US citizens, two Australians and one British national.
Police said they could not comment on the circumstances or possible causes pending an investigation.