Court-appointed trustee Irving Picard is alleging two dozen counts of fraud and misconduct against the London-based banking giant.
He has accused HSBC of helping Madoff's "Ponzi" scheme by creating a number of so-called feeder funds across the world and alleges that the bank ignored warnings from its own accountants that the financier's investment record was suspicious.
The bank last night said it would defend itself against the claims. A spokesman added: "HSBC is defending itself vigorously against Madoff-related claims that have been brought against it in various jurisdictions around the world.
"HSBC believes that the US court-appointed trustee's claims of wrong-doing are unfounded and it will defend itself vigorously against those claims as well."
Madoff is serving a 150-year term for a $65bn fraud. He admitted deceiving thousands of investors through a scheme that paid out using new investors' money rather than from profits.
The lawsuit against HSBC has been filed at the US Bankruptcy Court in New York. Picard named other defendants in the filing, including the management companies and providers of the feeder funds.
He alleges that the defendants were well aware of the signs of fraud that were already circulating around Bernard L Madoff Investment Securities (BLMIS).
HSBC had twice asked accountancy firm KPMG to identify concerns with BLMIS and KPMG twice reported serious risks already known to HSBC, Picard claims.
The lawsuit follows similar cases filed against JP Morgan Chase and UBS. Madoff admitted defrauding thousands of investors through his scheme, which had been running since the early 1990s.