Almost 20,000 viewers of the show have complained that Shetty has been subjected to racist abuse by her Big Brother "housemates".
Contestants on the show have mimicked Shetty's accent, while one contestant referred to her as "the Indian" and asked her if she lived in a shack.
In India, Shetty's treatment was front page news and provoked protests where effigies of the shows producers were burnt.
A statement from the Indian Foreign Ministry said: "The government of India has taken up the matter with the British government."
"I have not seen the show in question... but I would agree that we should oppose racism in all its forms"
British prime minister
A spokesman for Blair said that the response from viewers showed there was "no level of toleration in this country for anything that rightly or wrongly can be perceived as racism".
The shows biggest sponsor has said it is reviewing its endorsement of the series.
But the controversy has helped the programme's ratings. It pulled 4.5 million viewers on Tuesday, up from 3.5 million on Monday.
One member of the public in India, interviewed by Al Jazeera, said: "This is supposed to be reality and if this is reality in the West, then I think it is very sad."
Channel 4, the broadcaster of the show, issued a statement saying there has been a "cultural and class clash between Shetty and three of the British women in the house" but denied that there had been "overt racial abuse or racist behaviour" against Shetty.
The British police are reported to be investigating emails sent to organisers of the show containing "unspecified threats against a number of the housemates".
Gordon Brown, the British chancellor, is currently visiting India.
He told reporters: "I want Britain to be seen as a country of fairness and tolerance... anything that detracts from that, I condemn."
Participants in the show are locked in the "Big Brother House" for the duration of the show and have no contact with the outside world. They are said to be unaware of the public outcry their behaviour has caused.
Celebrity Big Brother is not available to viewers in India, but the country has its own similar show called "Big Boss".