BuzzFeed and other media reports were based on leaked suspicious activity reports (SARs) filed by banks and other financial firms with the U.S. Department of Treasury's Financial Crimes Enforcement Network (FinCen).
The revelations underscore challenges for regulatory and financial institutions trying to stop the flow of dirty money despite billions of dollars of investments and penalties imposed on banks in the past decade.
HSBC shares in Hong Kong fell as much as 4.4% to HK$29.60 on Monday morning, the lowest since May 1995, while StanChart dropped as much as 3.8% to HK$35.80, the lowest since May 25 this year.
The Hang Seng Index was down 0.4%.
HSBC and Standard Chartered, among other global banks, have paid billions of dollars in fines in recent years for violating U.S. sanctions on Iran and anti-money laundering rules.
More than 2,100 SARs, which are in themselves not necessarily proof of wrongdoing, were obtained by BuzzFeed News and shared with the International Consortium of Investigative Journalists (ICIJ) and other media organisations.
The files contained information about more than $2 trillion worth of transactions between 1999 and 2017, which were flagged by internal compliance departments of financial institutions as suspicious.
The ICIJ reported the leaked documents were a tiny fraction of the reports filed with FinCEN.
HSBC and StanChart were among the five banks that appeared most often in the documents, the ICIJ reported.
The SARs showed that banks often moved funds for companies that were registered in offshore havens, such as the British Virgin Islands, and did not know the ultimate owner of the account, the report said.
Staff at major banks often used Google searches to learn who was behind large transactions, it said.
In a statement to Reuters on Sunday, HSBC said "all of the information provided by the ICIJ is historical." The bank said as of 2012, "HSBC embarked on a multi-year journey to overhaul its ability to combat financial crime across more than 60 jurisdictions."
StanChart said in a statement, "We take our responsibility to fight financial crime extremely seriously and have invested substantially in our compliance programmes."