He also posted a picture showing how both his daughters were "badly bitten" all over their bodies.
Other passengers also reported seeing the insects on Air India flights, the Hindustan Times reported.
In another incident reported by the Times of India, an eight-month-old infant was bitten by bugs on a flight from Newark to Mumbai last Thursday.
Two days after Tonsekar's complaint, another passenger, Rohan, came forward on Twitter and wrote, "my wife and three kids [flew] business class AI 144 from Newark to mumbai; now they have bed bug bites all over their body; is this what we paid $10,000 for???"
Rohan said that once he arrived in India, his wife was prescribed 10 days of medication for the bites.
Following the reports, Air India told the Hindustan Times that the two aircrafts affected were grounded for one day each and fumigated, with seat covers replaced.