A British security source has told Reuters news agency that early indications do not suggest that the plane is the subject of a terror attack.
Stansted Airport has said that the diverted plane is in an isolated stand away from passenger areas.
It added that the airport is operating as normal.
Eurocontrol, Europe's air navigation safety watchdog, said "significant" delays are expected at Stansted Airport following an "incident with a 777 declaring an emergency":
Two Typhoon jets from RAF Coningsby have been scrambled to escort a passenger airliner.
The Pakistan International Airways jet has been diverted to Stansted airport which is the UK's designated counter terrorism airport.
Defence sources cannot yet say why the jets were scrambled to assist. The RAF carries out around a dozen such missions each year.
The passenger aircraft has now landed at Stansted.
Essex Police said the plane, which had departed from Lahore, had landed at Stansted. It is understood the incident happened around 10 minutes before the plane, flight number PK709, was due to land in Manchester at 2pm.
An RAF Typhoon jet has been scrambled after an incident on board a Pakistani passenger aircraft within UK airspace. According to Manchester Airport the aircraft, which is still in the air, is a Pakistan International Airlines passenger plane which was flying from Pakistan to Manchester.
– Ministry of Defence spokesman
"A Typhoon aircraft has been launched to investigate an incident involving a civilian aircraft within UK airspace."
An RAF fighter has been scrambled after an incident on a plane bound for Manchester from Pakistan.
– An Essex Police spokeswoman
"An incident has occurred on an aircraft. Police and partners are responding."
The aircraft, which is still in the air, is a Pakistan International Airlines passenger plane which was flying from Pakistan to Manchester, a Manchester Airport spokesman said.
An RAF Typhoon jet has been launched to investigate an incident involving a civilian aircraft in UK airspace. Reports said the aircraft was a Pakistani passenger plane which had been diverted from Manchester to Stansted.