In the film, The Hulk's alter ego Dr. Bruce Banner, played by Mark Ruffalo, is seen treating lepers.
Rituparna Sengupta, who lives in Kolkata, told the The Hindustan Times: "Kolkata has a rich culture and heritage, and a filmmaker should respect that.
"There are two scenes about India, and they only show slums. It could have been done in better taste."
Actress Neha Dhupia also expressed her concerns at the portrayal of India in Hollywood.
"It is disturbing to see the murky underbelly of India in Hollywood films. But before pointing it out to the west, we need to make efforts to change their perception about us."
According to The Hollywood Reporter the shanty town in the Bengali capital where Banner was staying was actually a set constructed in New Mexico.
A song by the Indian band Agnee will feature in the Hindi-dubbed version of The Avengers.
The Avengers Assemble, meanwhile, raked in over $200 million (£124m) in its opening weekend in the US, and is predicted to become the highest-grossing debut of all time.