French magistrates will examine whether the bank helped some clients to avoid paying taxes between 2006 and 2007.
The bank said it had been asked to deposit a bail bond of â‚¬50m (Â£39.6m).
"We will continue to co-operate with the French authorities to the fullest extent possible," it added.
On Monday Belgium prosecutors alleged that hundreds of the bank's clients moved money to offshore tax havens with the help of the bank.
HSBC's private banking arm, which is based in Switzerland, is under formal investigation in France, days after being accused of tax fraud by the Belgium authorities.