IndiGo placed an order for 180 Airbus planes worth $16 billion last year in the biggest jet order in commercial aviation history.
"Indigo has some rapid growth issues," said the report, a copy of which has been obtained by Reuters.
"The fast-growing induction plan of fleet in the organisation also needs to be reviewed in view of the serious findings recorded in the audit report."
The report by the Directorate General of Civil Aviation has pulled up almost every Indian airline for a shortage of instructors and slower training of both pilots and cabin crew.
There has also been suspected under-reporting of potential safety issues, including at IndiGo, it said.
IndiGo denied it was under-reporting incidents, saying it submits a "daily defect report" to the DGCA "and therefore, there is 100 percent reporting of all maintenance actions."
It also said it was addressing its staffing shortfall by training more captains and hiring pilots.
The airline said it would hold a news conference on Tuesday.
Details of the report's findings have been dribbling out for the past several days.
Kingfisher Airlines (KING.NS) and state-run budget carrier Air India Express are in "major financial distress", the report said, while Jet airways (JET.NS), Spicejet SPJT.NS and GoAir have "some financial distress issues".
The report said "a reasonable case exists" for withdrawal of Kingfisher's operating permit. The airline has grounded 20 of its 64 planes.
The agency, which has demanded a response from the airlines, said financial problems at some carriers could lead to safety compromises. It has asked the airlines to offer timelines to set things right.
(Reporting by Aniruddha Basu and Sanjeev Choudhary; Editing by Ted Kerr)
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