Police used a Taser gun to pacify the suspect during a struggle on the apron near Terminal 2.
Bomb disposal experts were called to examine a suspect package at the scene after the arrest.
One of the piers at Manchester Airport's Terminal Two was evacuated and parts of Terminal 1 were also cordoned off.
The airport said there would be disruption to flights but passengers should continue to check in as normal.
Greater Manchester Police said they were called to the airport after a man was seen acting suspiciously near aircraft.
In a statement GMP said: "At approximately 8.30am, police were called to Manchester Airport following reports that a man had been seen acting suspiciously in the apron area, where aircraft are parked, close to stand 26.
"Police attempted to arrest the man who struggled with officers. A Taser gun was then used to detain the man.
"The army bomb disposal unit have been called to examine a suspicious package that was found on the apron.
"A cordon has been set up and parts of Terminal 1 and Terminal 2 have been closed while officers deal with the incident."
A spokeswoman for Manchester Airport said: "Greater Manchester Police is currently investigating a suspicious package on the apron between Terminal 1 and Terminal 2.
"As a precautionary measure a police cordon is in operation and part of Terminal 2 and C Pier have been evacuated.
"There will be an impact on some flights due to leave Terminal 2 this morning, although every effort will be made to minimise disruption, and passengers should continue to report to the airport as normal."