IndiGo said its systems were down across the network since Monday morning, and that it expects operations at airports to be impacted as a result.
"All efforts are being made to resolve the issue at the earliest," IndiGo said in a statement.
IndiGo, owned by Interglobe Aviation Ltd, is the country's largest carrier with a nearly 50% share of the domestic market.
Travellers affected by the outage took to Twitter to raise concerns.
"IndiGo says systems down and huge queues till outside the main entrance gates in Mumbai T2," one user with the handle @Sathyantweets tweeted, referring to Terminal 2 at Mumbai's airport. "Chaos. No one knows when it will be resolved." IndiGo's outage comes as dozens of flights face delays or cancellations on Monday, according to reports, due to a decline in visibility because of hazardous air pollution shrouding New Delhi, home to India's busiest airport.
Interglobe Aviation's shares had risen 0.3% by 1215 local time (0645 GMT) in Mumbai, while shares in rival airline SpiceJet Ltd were down 2%.