The airline said in a statement that the flight turned around "due to loss in cabin pressure" and "regretted" what happened.
"During climb, crew forgot to select bleed switch due to which cabin pressurisation could not be maintained", a senior DGCA (Directorate General of Civil Aviation) official said.
Suddenly the oxygen masks dropped and passengers began to complain of headache and nose-bleeding.
A Mumbai-Jaipur flight of Jet Airways on Thursday left several passengers in a state of distress and an unpleasant flight experience.
Melissa Tixiera via Reuters
Television footage of video apparently taken by a passenger showed oxygen masks hanging from overhead compartments and passengers breathing through them. "I am surprised why the pilot switched the bleed off while taking off from Mumbai and when he switched it off, why he did not switch it on", said Saxena.
The flight - a Boeing 737 - immediately turned back and landed in Mumbai where the affected passengers, some of whom also complained of headaches, were offloaded and were attended to by doctors at the airport.
India's Ministry of Civil Aviation said in a tweet it had sought an "immediate report" from official agencies. The Times reported that India's Aircraft Accident Investigation Bureau has launched a probe into the incident, and the airline said it is "extending full cooperation".
The plane carrying 166 passengers landed safely. The plane had to return to the airport half-way. All guests were deplaned safely. According to the South China Morning Post, on New Year's Day, two pilots got into a brawl in the cockpit during a flight from London to Mumbai.
A hospital chief told the Indian Express that at least five patients had been taken to the hospital. He further said that during landing, there was extreme pressure in the flight and he kept covering his ears and holding the mask, and fell unconscious for 10 to 15 seconds.