Documents containing controversial information were obtained by the International Consortium of Investigative Journalists, The Guardian, Le Monde and CBS 60 Minutes, and published on Sunday.
The files revealed that HSBC advised some of its clients on how to conceal undeclared accounts, and provided services to international criminals.
The data was stolen by a computer expert who worked for HSBC's Geneva office in 2007, and in 2010, the French authorities that obtained the files shared them with the US International Revenue Service.
HSBC has previously been charged with violating US sanction laws and laundering money to Mexican drug cartels. The issue was resolved in a landmark civil settlement in 2012.
Senator Brown expressed his concern over the fact that US authorities have done nothing when they realized that the same institution had violated the laws for the second time.
"I intend on pressing regulators, the IRS, and the DoJ for answers," senator said.
HSBC is the world's second-largest bank and is headquartered in London. It has an international network of 6,200 offices in 74 countries, serving around 52 million customers.