Ravindra Gaikwad later told Indian reporters he had "hit him 25 times with my sandal" for "arrogance".
The MP had been told he could not fly business class because it was an all-economy flight, reports say.
Air India filed a police complaint and said it was considering a "no-fly" list for unruly passengers.
The MP told media: "I am not a BJP MP. I am a Shiv Sena MP and will not tolerate any insult. Let the employee complain. I will complain to the Speaker and other authorities."
The airline staff member told Asian News International that the MP had broken his glasses in the attack.
"When I told him what he was asking wasn't possible, he became abusive and started using foul language," he said. "God save our country if this is the culture and behaviour of our MPs."
The story was the top trending topic on twitter in India on Thursday.
Ashok Ganapathi Raju, the civil aviation minister, told reporters at parliament, "No citizen will behave like this. Physical assault won't be encouraged and will always be condemned."
Last year an Indian MP was arrested for alleging slapping an airline official at an airport in Andhra Pradesh after being told he could not board a flight with his family after the gate had closed.
The Shiv Sena party is a junior coalition partner in the Maharashtra state government, which is ruled by India's governing BJP.
Over time, it has acquired a reputation for promoting religious and ethnic chauvinism and has resorted to physical attacks against those its members and supporters oppose.
In 2015, Shiv Sena activists doused the head of an Indian think-tank in black ink in protest at his support for the launch of a book by a former Pakistani foreign minister.
An Indian MP beat an airline employee repeatedly with a slipper after being unable to get a business class seat on an Air India flight.