The IndiGo flight, with 174 passengers on board, took off from the Netaji Subhash Chandra Bose International Airport at 2:38 pm but returned to the bay at 2:57 pm after the Air Traffic Control saw smoke billowing from its left engine, a security official said.
"Full emergency was declared immediately and the flight landed safely," the official added.
All passengers were safe and the incident was reported to the Directorate General of Civil Aviation, IndiGo said.
The airline added that the passengers were accommodated in a different aircraft, which departed nearly two hours after the incident, at 4:56pm.
"The flight experienced high engine vibration in engine 2 immediately after take-off from Kolkata. The Captain-in-Command immediately alerted the base and took the decision to return to bay. All necessary SOPs were carried out."