The London-based telecoms provider said that it alerted police after carrying out a data security review.
However, a spokeswoman stressed that it had seen no evidence that the suspects had been involved with a high-profile cyber-breach last October.
Nearly 157,000 of TalkTalk customers' details, including bank account numbers, were stolen in the breach.
The unnamed suspects do not work for TalkTalk directly but are instead employed by Wipro, a local call centre provider, in Kolkata (Calcutta).
"Following the October 2015 cyber-attack, we have been conducting a forensic review to ensure that all aspects of our security are as robust as possible - including that of our suppliers," the company said.
"Acting on information supplied by TalkTalk, the local police have arrested three individuals who have breached our policies and the terms of our contract with Wipro. We are also reviewing our relationship with Wipro.
"We are determined to identify and deal effectively with these issues and we will continue to devote significant resource to keeping our customers' data safe."
News of the arrests was first reported by Channel 4 News.
The Indian company has said it has a "zero tolerance" policy on data theft.
"Wipro is working closely with the customer in the investigation and will continue to extend its full co-operation to the investigating authorities," it said.
"We are unable to comment on the matter that is currently under investigation."

SSAFA said there were more than 3,000 calls to Forcesline from serving troops last year, up from 1,600 in 2014.
The service was set up at the Army's request after four recruits died at its Deepcut Barracks in Surrey.
SSAFA said the rise in the number of calls "although not a cause for panic, is reason for concern".
The charity's chief executive, Air Vice Marshal David Murray, said: "Those who serve in our armed forces are by their very nature resilient characters. They are then trained to be the most robust versions of themselves, so for some asking for help can be a real challenge.
"It is interesting that the service men and women who are contacting us are choosing to come to SSAFA, rather than their own chain of command, as the 'grin and bear it' attitude within the serving community remains strong."
He said it was "imperative" that the welfare of service personnel welfare remained a priority and troops did not feel they had to "deal with their issues on their own".
"They have been there when our country has needed them and we must be there when they need us," he said.
A Ministry of Defence spokesman said: "The government is absolutely committed to the wellbeing of our armed forces and provides a wide range of support both during and after service.
"We enshrined the armed forces covenant in law and have introduced a raft of measures designed to improve service life.
"The government works in close partnership with the service charitable sector on these issues and we value contributions such as this."
SSAFA, formerly known as the Soldiers, Sailors, Airmen and Families Association, has a network of 7,000 volunteers providing support for serving personnel as well as veterans.
Between 1995 and 2002, four Army recruits died from gunshot wounds in unexplained circumstances at Deepcut, sparking allegations of bullying and abuse.
The Army said all of the deaths were suicides but, in each case, the families disagreed.
A second inquest is taking place into the death of one of those recruits, Private Cheryl James, more than 20 years after her death.
Among other things, the coroner will consider accusations that there were "shortcomings" with barracks policies on sexual behaviour, supervision of young women, drugs, alcohol and accommodation.
In total, the SSAFA helpline received 21,983 requests for help in 2015, up 6% on the year before.
TalkTalk has confirmed that three of its India-based call centre workers have been arrested.
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A confidential helpline has seen a nearly 90% increase in requests for help from serving military personnel, an armed forces charity has said.