A police spokesperson said as a precaution they had evacuated the airport.
Scores of people waiting at the airport to board flights to Wellington and Auckland were made leave the terminal around 11.30am.
Police were still working to establish the circumstances surrounding the threat and to speak with those involved.
The road leading into the airport was blocked by police, and passengers were unable to leave while investigations were under way.
Gisborne Airport issued a statement on Facebook at lunchtime warning travellers to expect disruptions to flights in and out of the airport for several hours.
It said anyone due to fly out or pick someone up from the airport today should call ahead and check for delays.
At least four departing flights have been delayed and one due to leave at midday has been cancelled. Others flying in have been delayed or diverted.
Those waiting outside the terminal said a fire crew had arrived.
The threat comes as thousands of revellers who attended the popular Rhythm & Vines festival, which ended last night, started to return home across New Zealand.
It is regarded as one of the airport's busiest days of the year.
So far, three Air New Zealand flights to Auckland have been delayed for several hours. A midday flight to Wellington has been cancelled, and a second to the capital has been delayed until mid-afternoon. A further four flights coming into the region from main centres have been delayed up to three hours.
A woman waiting for a flight to Wellington said travellers and staff ushered out of the packed terminal were now waiting under trees and in a nearby field while the emergency unfolded.
Emma Clarke said it was proving to be an annoying disruption, as her midday flight home had been cancelled and a second flight was hours away.
She said staff at the airport had not said anything about the evacuation to people waiting on the ground.
The only sign anything was amiss was when travellers were told a plane bound for Auckland was delayed because of a technical issue.
"Then everyone was made to leave the airport," Clarke said.
At that point everyone was forced to gather in nearby grounds under the sweltering midday sun while emergency services including police and firefighters arrived to investigate the threat to air travellers, she said.
