Videos online show huge pillars supporting the roof smashing into cars parked along the airport's Terminal 1.
All departures from the terminal have been temporarily suspended and check-in counters have been closed.
The incident took place at 05:00 (23:30 GMT Thursday), the authorities say.
Rescue operations are under way at the airport and the injured are being treated in hospitals.
The terminal underwent a massive renovation at the cost of billions of rupees and was inaugurated in March.
Heavy rains have lashed Delhi since Thursday, providing a much-needed respite from sweltering temperatures that the Indian capital was experiencing.
However this has led to waterlogging in some areas.
India's meteorological department forecasts that the city will continue to see "heavy to very heavy rainfall" over the weekend.
DM