It said the pilot was given its flight plan by the airline's Operations Dispatch Centre (ODC).
However, Auckland's air traffic control centre was "inadvertently given an earlier flight plan".
"Both routes were following an approved flight path and the aircraft had enough fuel for both routes," a Malaysia Airlines statement said.
"The safety of both passengers and crew were never compromised at any time.
"Malaysia Airlines is currently conducting its investigation in the flight plan submission.
"Safety is of the utmost priority for Malaysia Airlines and it adheres very strictly to all safety procedures and processes."
It is understood passengers on board the flight, which left at 2.23am Christmas Day, were not alerted to the mix-up.
Airways' internal safety team is also investigating.
"The flight plan the airline filed with us was going to Kuala Lumpur but via a slightly different route than the pilot was expecting," a spokeswoman said.
Airways will "work closely" with the carrier to find out how the confusion came about, the spokeswoman said.
Last year, 577 crew and passengers lost their lives on two separate Malaysia Airlines flights. Flight MH370 disappeared between Kuala Lumpur and Beijing for unknown reasons in March and MH17 was shot down by a Russian-made missile over Ukraine in July.