Swiss subsidiary HSBC Private Bank SA (Suisse), which is wholly owned by the Asia-focused banking giant, allegedly helped hundreds of clients cheat the Belgian state, a statement from the prosecutors said.
It is the latest in a series of international investigations into practices ranging from currency exchange rigging, Libor rigging and product mis-selling that has damaged the reputation of major banks.
Banking practices also had helped to spark the 2008 global financial crisis that led to a worldwide recession.
It said the allegations "date back several years and involve soliciting and managing the assets of wealthy clients, mainly from the Antwerp diamond industry."
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"The Swiss bank is also suspected of knowingly favouring and encouraging fiscal fraud, giving privileged clients to offshore accounts, particularly in Panama and the Virgin Islands."
Antwerp, a port in Belgian's northern Flemish-speaking region, is home to the global dealers syndicate for diamonds.
In 2012, Belgium's justice minister ordered an inquiry into a growing controversy over possible tax fraud among diamond traders in Antwerp after French authorities handed a list of dozens of dealers suspected of placing assets in Switzerland.