It was the second such incident in two days at the city's Netaji Subhas Chandra Bose International Airport.
The aircraft was moved to an isolation bay, and passengers were safely evacuated before personnel from the Central Industrial Security Force (CISF), the bomb squad and airport police searched the plane, the official told PTI.
No suspicious object was found during the search.
All prescribed security protocols were followed, and authorities suspected that the message had been written to create panic, the official said, adding that the matter was under investigation.
The latest scare came a day after a handwritten note threatening a bomb at a boarding gate was found in a women's washroom at the airport on Friday.
The two incidents within 24 hours prompted airport authorities to step up scrutiny of security arrangements, PTI reported.
Police are examining the passenger list and CCTV footage to identify the person who wrote Saturday's threat message, a senior officer of Bidhannagar City Police told PTI.