City National Bank is the latest major US company to admit it has lost customer data.
The bank says it lost data back-up tapes in April, while they were being transported to a secure facility by third-party data storage company Iron Mountain.
The sensitive data contained account numbers, social security numbers and other information, said the bank. It said it was not aware of any of the lost data being used to commit fraud or other crimes.
It is unclear whether the back-up tapes, covering an undisclosed number of customers, were encrypted. The FBI is investigating the data loss.
Iron Mountain was also responsible for losing Time Warner data back-up tapes in May, which contained information on 600,000 current and former employees.
CitiBank, Bank of America and MasterCard are among a number of US firms to have lost large amounts of customer data in recent months.