The incident, which took place on December 30 last year, comes nearly three months after the staff of the Gurgaon-based airline thrashed a passenger at the Delhi airport.
"IndiGo airlines threatened passengers to get down from aircraft otherwise they will drag out passengers using CISF at Patna," Prasad Nandurkar, a passenger and chief executive officer of a private engineering college in Maharashtra said in his FB post.
In the post, Mr Nandurkar also alleged that the airline first allowed boarding and later cancelled the flight.
IndiGo, however, in a statement said all the passengers cooperated and deplaned except for a group of 20 passengers who refused to deplane despite its staff "politely" requesting them to cooperate.
"IndiGo flight 6E-633 (Kolkata-Patna-Lucknow) scheduled to depart from Patna on December 30, at 8:20 pm was cancelled due to bad weather and low visibility. The visibility dropped to 50 meters at the time of scheduled departure."
"Keeping in mind the safety of passengers and staff, IndiGo cancelled the flight and, as a standard procedure, offered alternate flight option to all passengers and accommodation to transit passengers," the airline said.
"All the passengers cooperated and deplaned except for a group of 20 passengers who refused to deplane and demanded accommodation for every passenger. Our staff politely requested them to cooperate as we were directed by authorities to close operations at the earliest," it said.
The crew members "humbly" explained the situation and procedures on the part of the airline, and repeatedly requested for passengers' understanding and cooperation, the airline added.
Earlier this month, a Parliamentary panel slammed IndiGo for "discourteous and rude" behaviour of its employees towards passengers, saying it was an "institutional" problem, and urged the "market leader" to adopt a consumer-friendly approach.
The observations, made in the report by the Parliamentary Standing Committee on Transport, Tourism and Culture, followed a video that went viral last year showing IndiGo ground staff allegedly assaulting a passenger.
"The Committee observes that the problem affecting the airlines are not personal, it is institutional. An institution like IndiGo has to develop a consumer-friendly approach in dealing with their passengers," said the report.
It added, "The Committee believes that being a leader in market share, IndiGo needs to look inward and find out the reasons for the discourteous attitude and rude and indifferent behaviour of their employees, whether it is their cabin crew or the ground staff."
The panel emphasised that the "arrogant behaviour of employees should stop".