The secretive "hacker collective" had earlier been singled-out by Sony as the possible guilty party.
But a posting on Anonymous' blog said: "Let's be clear, we are legion, but it wasn't us. You are incompetent Sony."
The electronics giant has offered compensation to users who suffer fraud as a result of the theft.
Earlier this week, Sony sent a letter to the US Congress accusing Anonymous of being involved in the attack.
"Sony has been the victim of a very carefully planned, very professional, highly sophisticated criminal cyber attack," said the letter, signed by Sony America boss Kazuo Hirai.
He said that Sony had found a file planted on its network labelled "Anonymous" and bearing the group's slogan, "We are legion".
But Anonymous said that it had been framed by online thieves to throw law enforcement off track.
“Start Quote
End Quote Anonymous' statementWhoever broke into Sony's servers... clearly wanted Anonymous to be blamed for the most significant digital theft in history”
The group, which made headlines in December 2010 after it used software freely available over the internet to temporarily bring down the sites of MasterCard and Visa, said that its members were not credit card thieves.
"Whoever broke into Sony's servers to steal the credit card info and left a document blaming Anonymous clearly wanted Anonymous to be blamed for the most significant digital theft in history," the statement read.
Revenge attackAccording to Sony, the group targeted the company and facilitated the hacking in retaliation for the electronics giant's recent legal action against George Hotz.
The US-based hacker was accused of breaking copyright laws by devising a way to change the operating system on Sony PlayStations.
The case was eventually settled after Mr Hotz agreed not to repeat such behaviour in future.
Sony claimed that the massive data theft also coincided with a distributed denial-of-service (DDoS) attack on its website by Anonymous.
Kazuo Hirai, Sony America boss, said the company found a file on its network labelled "Anonymous" Denial-of-service attacks take servers down by overwhelming them with traffic.
But Anonymous denies all responsibility for allowing access to online gamers' data, including millions of credit card numbers.
"No one who is actually associated with our movement would do something that would prompt a massive law enforcement response," said the group's statement.
"On the other hand, a group of standard online thieves would have every reason to frame Anonymous in order to put law enforcement off the track."
