The service would be launched at 17 other airports by the end of June, the airline said in a release.
The facility would allow customers to check in, select seats and print their boarding passes for their flights without queueing up at check-in desks, the release said.
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Customers with check-in baggage can drop them at the check-in desks after printing their boarding passes.
According to the release, the kiosks would also be available for Singapore Airlines and SilkAir customers flying on Vistara-operated aircraft under code-share tickets.
With a fleet of 13 planes, the airline operates more than 530 weekly flights.