Carphone Warehouse said the security breach was discovered on Wednesday and that extra measures have been put in place to prevent further attacks.
The affected division operates the websites OneStopPhoneShop.com, e2save.com and Mobiles.co.uk and provides services to iD Mobile, TalkTalk Mobile, Talk Mobile and some Carphone Warehouse customers.
Carphone Warehouse said it was contacting all customers who may have been affected.
The company added that the customer information of Currys, PC World and the "vast majority" of Carphone Warehouse is held on separate systems and was not accessed during the attack.
We took immediate action to secure these systems and launched an investigation with a leading cyber security firm to determine exactly what data was affected.
The personal data of up to 2.4 million Carphone Warehouse customers, including bank details and encrypted credit card information, may have been accessed in a cyber attack.
The mobile phone retailer said a division of Carphone Warehouse was hit by the attack, in which data including names, addresses and dates of birth could also have been accessed.
The encrypted credit card information of up to 90,000 customers may have been accessed, a statement released by the firm warned.
We take the security of customer data extremely seriously, and we are very sorry that people have been affected by this attack on our systems. We are, of course, informing anyone that may have been affected, and have put in place additional security measures.
Twitter's share price was down 3.27% at $27.55 on closing last night.
The social network hit a record high of $73.71 in December 2013.
The firm is looking for a new CEO to replace Dick Costolo, who left on July 1 amid criticism of his growth strategy for the business.
Last night's share price places the company only marginally higher than its IPO price of $26 per share.
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I'm going to play for @krcgenkofficial this season on loan, it'd be great experience for me and I'm impatient to play at Cristal Arena. ?
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