"We take these types of allegations very seriously and are reaching out to the customer too as part of our investigation into the situation.
"We apologise sincerely if Megan felt she was spoken to unfairly."
The airline will be speaking to crew members individually who were aboard the flight.
Alatini has since removed the post from Facebook.
The TrueBliss star is employed by Air New Zealand and became a flight attendant four years ago.
The five-member Kiwi pop girl group, TrueBliss, found instantaneous and brief stardom after forming in April 1999, from the reality TV series Popstars.
Alatini went on to judge in the 2006 NZ Idol show alongside Iain Stables and Frankie Stevens.
The mother-of-three competed on the third season of New Zealand's Dancing with the Stars, finishing second.
The South African-born star married former All Black Pita Alatini in February 2000.