The attack, aimed at the military airbase at the Kabul airport, was launched when the Boeing 737 was getting ready for takeoff.
Reports said the rocket hit a target on the military side of the international airport, which led to counter-attacks by the Afghan security forces guarding the airport and suspected Taliban insurgents.
The passengers, crew and the SpiceJet aircraft of the no-frill carrier were not affected by the strike but the departure was delayed from the scheduled 1140 hours (local time) to 1500 hours due to the cross-fire. The flight landed safely at the IGI Airport here.
The attack has not deterred SpiceJet from stopping its services to Kabul, with an airline spokesperson saying it was "business as usual" for them.
SpiceJet operates to Kabul from Delhi one flight each on Tuesdays, Thursdays and Saturdays. While Air India flies six days, barring Wednesdays, to Kabul, the only Afghan carrier which flies into Delhi is private airline Kam Air.
The attack, which came soon after a terror strike on Karachi airport and a shootout at the Peshawar airport, led to the closure of Kabul airport for a few hours. The runway, the refuelling facilities and other operations were suspended during the period.
The Civil Aviation Ministry is likely to hold a meeting to discuss the safety of flight operations to Afghanistan, official sources said.