An ex-contractor at the Department for Work and Pensions had two discs with thousands of benefit claimants' details for more than a year, the DWP says.
The discs containing the data were unencrypted
The unencrypted discs revealed the type of benefits paid, but a DWP spokesman said they did not contain bank details.
The woman told the News of the World she forgot to return them after she stopped working for the DWP a year ago.
In October, two child benefit discs containing the personal details of 25 million people went missing.
The HM Revenue and Customs discs containing the entire child benefit database, unregistered and unencrypted had been sent to the National Audit Office - but they did not arrive.
The DWP discs in the latest incident contained names, addresses, dates of birth and National Insurance numbers.
They were part of a project aimed at encouraging people to switch from a giro to a credit transfer system.
It is believed there could be up to 9,000 names on each disc.
The government's reaction to this latest lapse is likely to be one of horror, says the BBC's Ian Palmer, coming so soon after the embarrassing loss of the child benefit discs.
He said it would also call into question its aim to push through a national identity card scheme.
The public would find it hard to back the scheme if government departments could not be trusted with sensitive information, he added.
A DWP spokesperson said the department took the security of customers' data "extremely seriously".
"Although there is no indication that any customers' data was compromised by this incident, we are investigating and will ensure the safe return of the information," he added.
On 18 October, HM Revenue and Customs sent two discs containing the entire child benefit database, unregistered and unencrypted, to the National Audit Office - but they did not arrive.
They were sent by courier from Tyne and Wear to the National Audit Office in London.
It is believed police fear the discs may have accidentally been thrown out as rubbish.
They have visited several tips around London to check what waste was delivered there.
The government has apologised and said there was no evidence the discs had fallen into the wrong hands. HM Revenue and Customs says they are probably still on government property.
But millions of families have been told to be on alert for fraudsters using their details, stored on the discs.
An interim report into how the discs went missing is expected in December.