Khan, who was interviewed by officials at Newark Liberty International Airport, told an Indian television station by telephone that Khan "is a Muslim name and I think the name is common on their checklist".
"Such incidents involving Indians due to their religion or nationality should not happen," he said. "We will not accept it."
The minister's intervention came after India's Sunday newspapers railed against the treatment of Khan, who has a huge following in the Hindu-majority country.
"Anger erupts over Shahrukh's insult," read the front page of the Hindi-language Dainik Jagran, while the Mail Today declared "Humiliating religious profiling of iconic star at US airport shocks India."
But US officials said that Khan, India's leading screen heartthrob, was subject only to routine procedures when he landed on Friday.
"The inspection process may include a more in-depth interview and baggage examination," the agency said in a statement, adding the incident had lasted little more than an hour.
Khan, who took part in celebrations in Chicago on Saturday marking India's Independence Day, said the way he had been treated left him "angry and humiliated".
Fox Star Studios has recently struck a deal to finance and distribute "My Name is Khan", a movie due out next year starring Khan as an Indian Muslim setting out on a journey across the US.
It features the contentious subject of racial profiling after the September 11, 2001 attacks.
Airport searches are a sensitive privacy issue in India, where similar outrage erupted last month when former president Abdul Kalam, also a Muslim, was frisked by US airline staff in Delhi before boarding a flight to New York.
Kalam was searched despite protocol at Indian airports exempting dignitaries from security checks, and the airline later apologised.
Fellow Bollywood stars sprang to Khan's defence at the weekend and told of their experiences at the hands of US immigration officials.
Irrfan Khan, who played the police inspector in last year's hit film Slumdog Millionaire, said that US screening staff seemed "threatened by any Muslim passport".
"I can understand America's need for caution after 9/11 but they also need to be a little more thoughtful about their methods," he said, adding he had been detained three times for questioning in various parts of the world.
Neil Nitin Mukesh said he had been detained in New York by an officer who appeared to believe he was too fair-skinned to be Indian and may have a false passport.
Shahrukh Khan's troubles were "yet another example of American paranoia post-9/11", director Kabir Khan said. "It saddens me to say this but I don't think the US will ever be cured of Islamophobia."
US Ambassador to India Timothy Roemer attempted to calm the furore by issuing a statement on Saturday describing Khan as a "global icon" who was a welcome guest in the United States.
Source: AFP Global Edition