The suspect was spotted wandering on the runway apron, a secure area where only staff are allowed.
Under the current high state of alert over terrorism, armed police were called in.
The man, of Asian appearance and understood to have little English, struggled with police when approached.
Officers had to use a Taser gun to disable him on the apron at Terminal Two.
He was arrested under the Terrorism Act, and is currently being held at a police station for questioning.
Army bomb disposal experts were called to examine a suspect package and carried out a controlled explosion on a black suitcase or briefcase.
The contents are now being examined.
A car believed to belong to the man is currently being recovered for further examination.
The security breach, at 8.30am, caused major disruption to passengers at the airport, with flights delayed.
Police placed a 600 metre cordon around the scene for three hours and one of the piers at Manchester Airport's Terminal Two was evacuated and parts of Terminal 1 were cordoned off.
Police later removed the cordon and said the operation was being scaled down with staff and passengers being allowed back in.
At one point Manchester Airport advised passengers not to travel to the airport, but later changed their advice, asking travellers to check-in for flights as normal.
Roads around the airport were closed for a time with traffic coming to a standstill.
Scores of passengers were stranded at the side of the road leading to Terminal 2.
The incident again raises questions about the level of security at UK airports.
National Air Traffic Services (Nats), which runs the UK's air traffic control system, said the number of flights in and out of Manchester had been restricted for a time but that the restrictions had now been lifted.
A Nats spokeswoman added: "There will be some delays to passengers but it is hoped that services will be back to normal soon."
The Department for Transport (DfT) said today it would be investigating the Manchester airport incident.
The department has overall responsibility for airport security and lays down a constantly-updated National Aviation Security Programme.
"We will want to know exactly what happened at Manchester and will be investigating," said a DfT spokesman.
So-called 'air-side' areas of airports are supposed to be secure although lapses in security have been exposed on several occasions by undercover reporters.
Manchester Airport said security was dealt with in-house but would give no further details about their security arrangements at the site.
A spokeswoman for the Airport said: "We are working closely with the police to establish the full facts of the incident."
Passengers at the airport said hundreds of people were now waiting in the terminal to collect their luggage.Ashley Wadeson, 19, from Leigh, who arrived on a nine hour flight from Calgary, Canada, this morning, said: "There were hundreds of people waiting to collect their bags. We waited for about an hour. Nobody told us anything." Reuse content