Fears were initially raised over "a possible device on board" by the pilot on board flight QR23 from Doha, Qatar, as it approached the airport.
Dramatic video footage and photos showed an RAF jet accompanying the Qatar Airways Airbus A330 as it made its descent , while passengers reported a man being removed from the plane after it landed safely.
Less than hour after the first reports, Greater Manchester Police confirmed the arrest was related to a suspected hoax.
Before confirming the passenger had been arrested on suspicion of a hoax threat, GMP said: "A passenger has been taken off the plane by officers at Manchester Airport. We will work to get others off as swiftly and safely as possible."
Qatar Airways said 269 passengers were on board.
The airline said in a statement: "Qatar Airways can confirm that flight QR23 from Doha to Manchester, an Airbus A330-300, landed safely at Manchester Airport ahead of its scheduled arrival time of 1315.
"There were 269 passengers and 13 Qatar Airways crew on board.
"The crew on-board had received a threat about a possible device on board and Qatar Airways immediately took all the necessary precautions to alert British authorities.
"The crew is now fully assisting police at the airport with their inquiries. The safety and well-being of our passengers and crew is our top priority. As this is a matter of a police investigation, we cannot comment further at this time."
Witness Paul Bell, who was on his way to the airport in a taxi, told Sky News that he saw the Typhoon, from RAF Coningsby in Lincolnshire, meet the passenger plane.
He said: "We heard the fighter jet circling over Stockport and literally 10 minutes later we saw the plane coming in being followed by it.
"We saw the Typhoon coming in, literally flying around the aeroplane.
"It then pinged up on the sat nav that the airport is on lock-down."
An RAF spokesman said: "We can confirm that Typhoon aircraft were launched from RAF Coningsby in their quick reaction alert role this afternoon to investigate a civilian aircraft whose pilot had requested assistance.
"The aircraft was escorted to Manchester where it landed safely. This incident is now being handled by the civilian authorities."
Manchester Airport said nine incoming flights had to be diverted to other airports, with five of these landing at Leeds Bradford airport.
One of the flights that landed on time at Manchester once the emergency was over was the plane carrying Manchester United back from Florida where the team has been engaged in a pre-season friendly tournament.
"There are a few minor delays to outgoing flights but we're pretty much back to normal," said an airport spokesman.