The law has sparked nationwide protests that have left at least 27 people dead, and stoked fears that India's 200 million Muslims will be marginalised.
Speaking at an event in New York, Microsoft boss Satya Nadella implied the law could stop a talented immigrant from making a mark India, as he had done as a new arrival in the United States, according to a transcript of his remarks tweeted by BuzzFeed editor-in-chief Ben Smith.
"I would love to see a Bangladeshi immigrant who comes to India and creates the next unicorn in India or becomes the next CEO of Infosys," Nadella said, referring to an Indian IT giant.
"If I had to sort of mirror what happens to me in the US, I hope that's what happens in India."
Nadella was born and educated in Hyderabad before moving to the US to do a masters degree. He joined Microsoft in 1992 and later became a US citizen. Nadella's comments sparked social media storm in India.
Ramachandra Guha, a renowned historian detained at a recent protest, tweeted: "I am glad Satya Nadella has said what he has. I wish that one of our own IT czars had the courage and wisdom to say this first. Or to say it even now."
But Meenakshi Lekhi, a lawmaker from Modi's ruling Bharatiya Janata Party, said Nadella's comments were a "perfect example" of how the "literate need to be educated".
"Precise reason for (the law)... is to grant opportunities to persecuted minorities from Bangladesh, Pakistan and Afghanistan," she tweeted.
Nadella was less critical in a statement issued Tuesday by Microsoft India.
"Every country will and should define its borders, protect national security and set immigration policy accordingly," the statement quoted him as saying.
"I'm shaped by my Indian heritage, growing up in a multicultural India and my immigrant experience in the United States. "My hope is for an India where an immigrant can aspire to found a prosperous start-up or lead a multinational corporation benefitting Indian society and the economy at large."