Officers boarded Pakistan International Airlines flight PK709, which had been due to land at Manchester, after it was diverted to Stansted Airport.
Two men, aged 30 and 41, are being held on suspicion of endangerment of an aircraft, Essex Police said.
A PIA spokesman said all passengers on board were safe.
The plane reportedly left Lahore - the capital of the Pakistani province of Punjab - at 09:35 local time. It was due in at Manchester at 14:00 BST.
BBC defence correspondent Jonathan Beale said there was a suggestion there had been threats on board during the flight, involving some sort of weapon or bomb - although this was unconfirmed.
However, one passenger told the BBC that the pilot told them there had been threats.
Stansted Airport said the pilot had alerted the authorities to the incident, but it did not say what that incident was.
A spokesman for the airport said passengers were being taken off the plane.
"They will be taken to a reception centre in the airport where police may wish to interview them about what they have seen," he said.
"At some point police and the airline will arrange for their onward transportation to Manchester."
Stansted Airport earlier said on Twitter that it was operating normally.
A Manchester Airport spokesman said: "A Pakistan International Airlines aircraft which was due to land at Manchester Airport at 13.30 BST today has been diverted to our sister airport London Stansted, where the authorities are investigating."
Mashhood Tajwar, a spokesman for Pakistan International Airlines (PIA), said the incident followed a call to air traffic control.
He said that about 20 minutes to half an hour before landing, information received by air traffic control in Manchester indicated there might have been "some security threat".
"But so far it has not been ascertained what was the real motive behind that call," said Mr Tajwar.
He added: "The plane was diverted to Stansted and it has landed safely over there and all passengers are safe, and they have disembarked."
PIA said there were 308 passengers on board, as well as 14 crew including pilots, with a mixture of Pakistani and British passport holders.
bbc.co.uk