The woman said she had received an apology from the airport four days later.
"It's wasn't satisfactory. To me, the safety of the people that work there, and the public, wasn't paramount. It could have been much, much worse, imagine if [the ceiling fell] on a newborn baby or something.
"It's actually quite a horrific thing to happen. The building is obviously not being kept up to health and safety regulations."
Airport chief executive Nick Story said rainfall had compromised a small area of external roofing in the corner of the southwest corner of the terminal building.
"Unfortunately, the ceiling tiles collapsed under the weight of rainwater, with debris falling on a young lady who was waiting to board an early morning flight with her mother."
He confirmed the area had earlier been isolated and re-opened to the public.
"After the rainfall in March, the problem area was attended by a contractor who secured the area and appeared to have remedied the problem. However, as we discovered during heavy rainfall in April, the actual leak which appeared in March had obviously not been properly contained."
He said the affected area was "isolated immediately" after the incident.
"The work includes the fitting of a new colour steel deck roof to the entire viewing area to restore the water tightness of the roof.
"As it is a health and safety issue, the remedial work is automatically an urgent priority.
"It would not have been appropriate for us to wait for the proposed terminal development project to fix the problem."
He said the airport had been in contact with the 13-year-old girl, her mother and father, and another customer, to offer "our sincere apology for the very distressing and unfortunate event".
Last month, the airport announced a $5 million terminal upgrade and a new name - Ahuriri Airport Hawke's Bay.
"These very unfortunate events highlight the tired state of our terminal facilities and support our proposed terminal development project as reported by Hawke's Bay Today."
A WorkSafe spokesman said he could not find any record to suggest the organisation was notified of the incident.