The Kolkata-based workers were arrested earlier this month following a data security review by the London-based firm, which then alerted Indian police.
The arrests came months after TalkTalk was hit by a high-profile hacking in October last year when personal details of its customers were compromised.
But the company have indicated that the latest arrests in India are not related to last year's data breach.
"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. 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," TalkTalk said in a statement.
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News of the arrests was first reported on Britain's 'Channel 4 News' last evening.
It reported that Indian police had made the arrests over the last fortnight in relation to allegations of theft of customers' data and using it to con them out of thousands of pounds.
"Wipro is committed to maintaining the integrity and confidentiality of all customer data and has a zero tolerance policy on securitybreaches," Wipro said in a statement.