The information includes phone numbers, addresses, credit card numbers and banking records, and they were leaked from Kookmin Bank, Shinhan Bank and several other institutions, Yonhap said.
"We launched a probe into Kookmin Bank in connection with the suspected data leak, and 14 other financial firms were ordered to do an internal inspection," prosecutors said in a statement.
The customers included minister-level officials and celebrities.
The leakage occurred when the financial institutions shared customer information with credit card companies, whose customer data was also leaked, Yonhap said.
Officials are pushing for more regulations to deal with bank security, including a restriction on what staff members can access client information.