A criminal investigation was launched yesterday.
In a statement on its website, TalkTalk said it was too early to know how much data had been stolen.
TalkTalk said: "We would like to reassure you that we take any threat to the security of our customers’ data very seriously. We constantly review and update our systems to make sure they are as secure as possible and we’re taking all the necessary steps to understand this incident and to protect as best we can against similar attacks in future. Unfortunately cyber criminals are becoming increasingly sophisticated and attacks against companies that do business online are becoming more frequent."
The phone provider has also contacted all major banks, which will be monitoring for any suspicious activity on customers’ accounts.
Cyber security consultant and former Scotland Yard detective Adrian Culley told BBC Radio 4's Today programme that a Russian Islamist group had posted online to claim responsibility for the attacks.
He said hackers claiming to be a cyber-jihadi group had posted data that appeared to be TalkTalk customers' private information - although their claim has not yet been verified or investigated.
PRWeek was unable to contact TalkTalk's press office for further information.