An airport official said the incident occurred in the afternoon when the two aircraft, belonging to Jet Airways, brushed against each other while "taxiing out" to runway 29.
The official said the passengers and crew on-board both the flights numbered over 200.
According to a Jet Airways spokesperson, the two Jet Airways aircraft -- operating flight 9W 603 from Delhi-Srinagar and 9W 730 from Delhi-Patna -- were involved in a ground incident during taxi, while preparing for departure from IGI Airport.
"The aircraft are currently being inspected by the Jet Airways engineering team. The airline has reported the event to the regulatory authorities. Both sets of crew have been de-rostered pending investigation."
The aviation regulator, Directorate General of Civil Aviation, has ordered an enquiry into the incident.