The Ireland front-rower was thought to be using his laptop after passengers were told to stop using electronic equipment before take-off.
Healy was made to take the next flight with the same airline and the 29-year-old has since linked up with the rest of the Leinster squad in South Africa.
"The issue related to a misunderstanding around the use of a laptop during the approach to take-off," a spokesman said.
"Cian disembarked the plane and took the next available flight to Cape Town with the same airline.
"Cian apologised sincerely to all concerned at the time for any inconvenience caused."