Speaking to media, an Air India official said that the immigration system server was down for more than 40 minutes since 12.20 am.
At around 1 am, the official also said that crew for three Air India flights were stuck.
The official said that no timeline has been given by immigration authority to resolve the issue.
A passenger, who was waiting for the immigration check, said there has been a long delay due to server issues.
A public announcement was also made at the airport about the server problem and that personnel have started doing manual checking process, according to the passenger.
Most of the passengers took to Twitter to complain about the issue.
The incident comes a day after Air India's Passenger Service System faced technical glitches and remained non-functional for more than five hours.
The system glitch on Saturday morning had also resulted in the delay of scores of Air India flights.
The Indira Gandhi International Airport is the busiest airport in the country.
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