Among them Pravin Tonsekar, who sat in the business class seats for a 17-hour flight Tuesday with his wife and kids.
"All our seats infested with bed bugs," he said in a Tweet. "Sir , have heard of bed bugs on trains but shocked to experience on our maharaja and that too business."
Air India replied with an apology.
On Wednesday, Twitter user @roscrow reported bed bug bites all over his wife and kids' bodies after a flight from Newark to Mumbai.
"Is this is what we paid $10,000 for???" he said.
An eight-month old baby was reportedly also bitten on another flight, Times of India reports. The airline said it is investigating.
Click here to follow Daily Voice Garfield-Lodi and receive free news updates.