Police say the man got into an argument with a Spirit Airlines employee at Terminal B.
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The suspect told the employee he was coming back with a bomb and then returned a short time later carrying a bag, according to the NYPD.
The ticketing area of Terminal B was temporarily evacuated.
The NYPD Bomb Squad was called in as a precaution to identify the package.
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The suspect, identified as 70-year-old John Park of Farmington, Michigan, was quickly taken into custody.
No explosive was found and no one was injured.
The Port Authority said the airport was functioning normally by 9:30 a.m.
Port Authority police interviewed the man and charges were pending.