The India-born executive said what is happening is "sad" and he would love to see a Bangladeshi immigrant succeed in the country's technology industry. Mr Nadella grew up in Hyderabad - India's technology hub - but is now an American citizen.
His comments come amid ongoing, sometimes violent, protests against the law. The Citizenship Amendment Act (CAA) has been criticised as it is seen as discriminating against Muslims.
Speaking at a Microsoft event for editors in New York, Mr Nadella said: "I think what is happening is sad, primarily as sort of someone who grew up there... I think it's just bad," according to BuzzFeed.
"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," he said.