The actor was reportedly detained for around two hours at White Plains airport near New York.
Khan was on the way to Yale University for a function when he was stopped.
This "policy of detention and apology by the US cannot continue", External Affairs Minister SM Krishna told the BBC.
US customs and border protection authorities later expressed "profound" apologies for the incident.
Peter Vrooman, spokesman for the US embassy in Delhi, also said they were sorry "if Mr Shah Rukh Khan experienced an inconvenience or delay".
In 2009 the My Name is Khan actor was detained for two hours at Newark airport and was released after the Indian embassy in the US intervened.
The actor suggested then that he was stopped because he had a Muslim name. US customs officials said he had not been detained, only questioned.
Members of the Indian film industry have also come out in support of the actor, with composer Javed Akhtar saying: "All that the US immigration authorities need to know about Shah Rukh Khan, they can find it at the touch of a button."
The Bollywood star was released from detention after Yale University contacted homeland security and customs officials.
Speaking to students at Yale, Khan joked about the incident, saying: "They [immigration officials] always ask me how tall I am and I always lie and say 5 foot 10 inches. Next time I am going to get more adventurous. [If they ask me] what colour are you, I am going to say white."