An "administrative error" was blamed for the incorrectly addressed letters containing confidential information relating to the pension payments of 26,000 customers.
The DWP learned of the error on 7 May when customers started receiving letters sent in error, according to a spokeswoman.
"We were sending out letters to customers letting them know what their weekly pension payments next year would be," she said.
"Some of those customers received letters intended for someone else. As soon as we found out we acted immediately and launched an investigation."
The spokeswoman added that the department had apologised to affected customers and that the DWP "takes issues of customer security very seriously".
Almost 100 organisations have reported data security breaches in the six months since HM Revenue & Customs reported the loss of two discs containing 25 million child benefit records.
Information Commissioner Richard Thomas said that the inexcusable security breaches include 62 within the public sector, 28 in the private sector and four at voluntary and charitable bodies.