Flight 9W 339, which had taken off from Mumbai at 2.55 am with 115 passengers and seven crew members, was diverted to Ahmedabad airport around 3.45 am.
The Boeing 737-900 plane was parked at a remote bay and all 122 safely deplaned, a Jet Airways spokesperson said.
The note, allegedly placed by Mumbai-based Gujarati jeweller Birju Kishore Salla, stated that there were hijackers and a bomb in the cargo area, officials said.
The reference to POK made investigators suspicious because Pakistan-based terrorists call the area 'Azad Kashmir', an official said.
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Salla, who is in his late 30s and belongs to Gujarat's Amreli district, was a repeat offender who usually travelled business class and appeared to have a grouse against the airline.
He had carried a cockroach in an earlier trip and blamed the airline. However, the airline had let him go after taking an assurance that he would not repeat the offence, an official privy to the investigation said.
Union Civil Aviation Minister Ashok Gajapathi Raju said he was advising airlines to put him on the no-fly list immediately, in addition to other statutory criminal action.
"I am informed that the person responsible for Jet flight 339 (Mumbai-Delhi) incident causing the landing at Ahmedabad today morning has been identified," Raju said in a tweet but did not identify him.
Security officials said nothing was found after a thorough check of all the passengers and their bags.
The flight was "diverted to Ahmedabad following declaration of an emergency as per established security procedures, due to the detection of an onboard security threat", the Jet Airways spokesperson said.
Giving details of what had happened, Ahmedabad Airport Director Manoj Gangal added that the flight was allowed to make an emergency landing on the pilot's request.
PTI correspondent Rajkumar Leishemba, who was on board, said all the passengers were deplaned and screened. They were profiled, their photographs taken and personal details sought, including their last overseas visit.
After more than six hours at the airport, the flight carrying the passengers took off for Delhi around 10.30 am, he said.
The note, with a para in Urdu on the top and English at the bottom, was shared by a senior official.