HSBC's private bank has major operations in Switzerland, London and Hong Kong, and its Chief Executive Peter Boyles is based in the lakeside Geneva office. The office has a few hundred staff, who continued to work on Wednesday.
"We have cooperated continuously with the Swiss authorities since first becoming aware of the data theft in 2008 and we continue to cooperate," HSBC said in a statement.
It declined further comment. The bank has said compliance and controls at its Swiss private bank in the period up to 2007 fell short of requirements, but said the business had been transformed in recent years.
Swiss financial regulator FINMA, which had already investigated HSBC and criticised its internal controls in 2011, said it was aware of the proceedings by the Geneva prosecutor and was in contact with HSBC about it.
Read MoreHSBC media leaks are'tip of iceberg': Whistleblower
HSBC's main concern may be that U.S. authorities could look at re-opening a 2012 deferred prosecution agreement with the bank, which followed a $1.9 billion fine after it was found to have helped move hundreds of millions of dollars in illicit drug money through the U.S. financial system.
The disclosures about the Swiss bank have sparked a political row in Britain over practices at HSBC and whether tax authorities had done enough to pursue possible wrongdoers.
HSBC shares were 0.6 percent firmer at 606.7p by 1155 GMT, having slipped two percent since the first reports based on the leaks were published 10 days ago.
HSBC Chief Executive Stuart Gulliver said recent allegations had been "painful". The allegations are likely to overshadow HSBC's annual results on Monday and Gulliver and Chairman Douglas Flint are due to testify to British lawmakers on the Swiss scandal on Feb. 25.
Read MoreUBS warns on Swiss franc strength, doubles dividend