Almost 10,000 viewers have complained about the treatment of Shetty, 31, who has been called a "dog" since the reality television series started barely two weeks ago.
The controversy made headlines in British and Indian newspapers on Wednesday and has even spilled on to the floor of the House of Commons, Britain's lower chamber of parliament.
Police in Hertfordshire, north of London, said two emailed threats had been sent to the show's broadcaster Channel 4.
"(They) contain unspecified threats against a number of the housemates. Police are currently looking in to the e-mails," a spokesman said late on Tuesday.
Detectives also received a telephone call complaining about "alleged racist behaviour" on the programme, he said. The caller was referred to the media watchdog Ofcom.
Shetty, an A-list Bollywood actress, has been reduced to tears in the "Big Brother" house, a purpose-built complex of rooms and a garden where the nine remaining housemates are living.
Ofcom has received 7,600 complaints from viewers concerned that housemates, including reality TV star Jade Goody, former beauty queen Danielle Lloyd and ex-S Club 7 singer Jo O'Meara, were victimising Shetty, media reported on Wednesday.
A further 2,000 email and telephone complaints were made directly to Channel 4, they said.
The broadcaster said it took matters of racism and bullying seriously. "Shilpa herself has not voiced any concerns of racial slurs or bullying against her," Channel 4 said in a statement.
The boss of Carphone Warehouse, a mobile phone retailer, said his firm was reviewing its sponsorship of the programme, according to the Times.
"The sponsorship is constantly under review. Clearly, we are against racism," Charles Dunstone told the paper.
Lawmaker Keith Vaz put forward an early day motion in parliament, saying: "We would not tolerate this kind of racism on any other type of television programme".
Filmed by hidden cameras, the antics of the housemates can be watched 24 hours a day, with highlights played every evening.
The housemates alone remain unaware of the furore in the outside world which -- if nothing else -- will likely boost the show's viewing figures.
The Indian government is also trying to collect information about alleged racist remarks against Shilpa Shetty on the British TV reality show "Celebrity Big Brother", said Minister of State for External Affairs Anand Sharma.
"Racism has no place in civilian society. India has, throughout, thrown out any kind of racism and discrimination. We are trying to collect the information," Sharma told reporters here today.
Viewers in Britain have complained that Shilpa, who is participating in the show which has a group of celebrities cooped up in a house with no access to the outside world, is being subjected to racial abuse by fellow housemates.
Monday night's show, for instance, featured scenes of participants picking on Shilpa for her cooking skills.
Former S Club 7 member Jo O'Meara made fun of Shilpa's Indian accent and complained that she had touched food with her hands. He was joined by model Danielle Lloyd. She said: "They eat with their hands in India, don't they - or is that China? You don't know where their hands have been."
During her time in the house, another contestant Jackiey repeatedly referred to Shilpa as "the Indian" and never pronounced her name correctly.
The show went on air Jan 2.