The deadly incident happened late Wednesday as the Airbus A319 was being towed backward from the parking bay in preparation for taxiing out, said Anil Mehta, an Air India official.
The engineer, Ravi Subramanian, was standing near the landing gear under the plane's nose as he supervised the process, Mehta told CNN.
Passengers had boarded the aircraft for a flight to the city of Hyderabad. It wasn't clear if any of them saw what happened.
Air India officials declined to give any further details, saying the country's civil aviation regulator is investigating the engineer's death.
Airline insists it follows safety procedures
"We are deeply saddened and regret the tragic incident at Mumbai airport yesterday evening," Air India Chairman Ashwani Lohani said in a statement, offering his condolences to Subramanian's family.
The Times of India newspaper cited airline sources as saying that Air India staff had followed an irregular engine start-up procedure because the plane's auxiliary power unit wasn't working.
"Air India follows all standard safety procedures and parameters," Mehta said in response to the report.
The incident is believed to be the first of its kind involving an aviation worker in India.
The only remotely similar case was 20 years ago, according to the Times of India, when a man used a borrowed airport pass to ride his moped across the runway in Hyderabad and was sucked into an aircraft engine.