The Air Nelson Q300 aircraft was requested to return to Auckland as a precaution.
The aircraft was then cleared by Aviation Security and returned to Napier, landing two-and-a-half hours behind schedule at 2.15pm, the spokeswoman said.
No other flights were delayed as a result of the threat.
An Auckland Airport spokesman said the airport's runway was closed between 11.05am and 11.35am following the "possible security threat''.
Counties Manukau District Police Communications Manager Kimberley Mathews said a 57-year-old woman was arrested in relation to the incident and charged with communicating false information.
She is due to appear at Manukau District Court on Monday.