An Aberdeen woman who asked for her bank statement was sent details of 75,000 other customers.
Stephanie McLaughlan said the blunder was "terrible negligence"
Stephanie McLaughlan, 22, was sent the financial details by Halifax Bank of Scotland (HBOS).
She received five packages each containing 500 sheets of 30 customers' names, sort codes and account details.
HBOS apologised and said it was carrying out an investigation. The Information Commissioner's Office (ICO) said it would probe the "negligence".
Ms McLaughlan said: "These packages were just dumped on my doorstep one day and I was really shocked because it was obvious the bank did not have a clue they had left them in my house or their contents.
"It was really shocking they made that mistake."
She added: "I think I'll probably be changing to another bank pretty soon because it is terrible negligence on their part."
HBOS said in a statement: "We are treating this matter very seriously and are investigating in full.
"This is a very specific, isolated incident and we will take steps to ensure there is no security issue for customers as a result of this matter.
"We apologise for any concern this has caused customers."
Ken Macdonald, ICO's assistant commissioner in Scotland, said: "It would appear that HBOS has been negligent with bank statements which contain important personal information about their customers.
"Clearly, where personal information is not processed and stored securely, there is a risk that it can fall into the hands of criminals.
"The Information Commissioner's Office takes breaches of people's privacy very seriously and we will be contacting the bank about this."
HBOS was formed in 2001 with the merger of the Halifax and Bank of Scotland and has millions of customers.