Passengers of the flight wanted the family to be allowed on board, witnesses said.
Aviation Minister Jyotiraditya Scindia on Monday warned IndiGo airlines after a spiralling backlash over not allowing a child with special needs to board a flight with his family at the Ranchi airport over the weekend.
"There is zero tolerance towards such behaviour. No human being should have to go through this! Investigating the matter by myself, post which appropriate action will be taken," the minister wrote on Twitter.
The aviation regulator Directorate General of Civil Aviation (DGCA) has also asked IndiGo for a report.
The action comes after the harrowing ordeal of the family was widely shared on social media, triggering massive outrage.
IndiGo, in a statement, said the child posed a threat to other passengers' safety. It stressed that it takes pride in being "inclusive" and refuted suggestions of discriminatory behaviour.
"In-view of the safety of passengers, a specially-abled child could not board the flight with his family on May 7, as he was in a state of panic. The ground staff waited for him to calm down till the last minute, but to no avail," said the airline.
Manisha Gupta, a fellow passenger and a witness to the scene, wrote about the incident in an elaborate Facebook post.
The IndiGo manager, said Ms Gupta, kept shouting and telling everyone that the "child is uncontrollable".
"The only person who is in panic is you," Ms Gupta quoted a fellow passenger's retort to the airline manager.
The family, said the airline, was provided a hotel stay, and they flew the next morning to their destination.
A group of doctors, travelling on the same flight, offered to provide full support to the child and his parents if any health episode were to occur mid-air, said Ms Gupta in her post.
Ms Gupta noted how other passengers rallied around the family.
They held up their mobile phones, said Ms Gupta, with news articles, Twitter posts on Supreme Court judgments on how no airline could discriminate against passengers with disabilities.
"In those 45 minutes of argument, temper, rage and contestation, the three (the family) had not once lost their dignity or raised their voice or spoken one irrational word," said Ms Gupta.