The pair were removed from a Pakistan International Airlines flight which landed safely after being diverted from Manchester to Stansted on Friday afternoon.
Officers arrested them on suspicion of endangering an aircraft.
A police statement said: "Essex Police have boarded a passenger plane diverted to Stansted Airport and two men have been arrested on suspicion of endangerment of an aircraft.
"They have been removed from the plane."
The Ministry of Defence scrambled a Typhoon jet after the incident was reported around 10 minutes before the plane was scheduled to land in Manchester.
At this stage it is understood the incident is not terrorism-related.
There were almost 300 passengers on the flight.
Manchester Airport said: "A Pakistan International Airlines (PIA) aircraft which was due to land at Manchester Airport at 1.30pm today has been diverted to our sister airport London Stansted, where the authorities are investigating. The plane - flight number PK709 - was travelling from Lahore and had 297 passengers on board."
Stansted Airport said passengers were being taken off the plane.
"They will be taken to a reception centre on the airport where police may wish to interview them about what they have seen," a spokesperson said.
"At some point police and the airline will arrange for their onward transportation to Manchester."