Authorities of the airport, the busiest in India, said it had suspended departures from the affected terminal until at least Friday afternoon and promised compensation to the victims.
The roof caved in at the pick-up and drop-off area outside Terminal 1, which handles domestic flights, at around 5 am on Friday (2330 GMT Thursday), the airport authorities said.
Images from the scene showed cars crushed under giant pillars.
At least one person was killed and six were injured, the NDTV news channel and news agency PTI reported.
The victims were in the vehicles struck by the pillars, according to NDTV.
Flights operating from Terminal 2 and Terminal 3 were unaffected.
Heavy rains and strong winds lashed the Indian capital for several hours overnight, flooding swathes of the city.
June marks the start of the monsoon season in South Asia, which lasts until around September.
