Security personnel made the decision to cancel all flights after crew on board EasyJet flight EZY883 raised the alarm at around 10.25am on Tuesday.
The Scotsman understands a note found to have been written within the plane during the flight prompted the pilot to contact the authorities.
Some 140 passengers who were on board were interviewed by police but the culprit is still being sought.
They were aksed if they had used the toilets during the flight.
The flight had just arrived from Gatwick and was delayed disembarking on arrival as a precaution, “due to additional security checks”, EasyJet said.
The airport’s runway was out of action for around 22 minutes, but reopened at 10.55am.
The incident was stood down as soon as emergency services arrived on board the plane.
A Police Scotland spokesman said: “All the passengers and crew disembarked and the aircraft was searched following a security alert reported by the crew.
“Nothing was found.
“All passengers were spoken to by officers.
“The circumstances surrounding the nature of the security alert will continue to be investigated.”
In a statement, a spokesperson for EasyJet said: “EasyJet can confirm that passengers on flight EZY883 from London Gatwick to Glasgow was delayed disembarking on arrival in Glasgow, purely as a precaution, due to additional security checks.
“The passengers have been disembarked and taken into the terminal. The safety and security of its passengers and crew is always EasyJet’s highest priority and we would like to thank passengers for their understanding.”
A Glasgow Airport spokesman said: “The incident was assessed following established procedures, after which we were able to open.”