Mr Biden said his lawyers had been informed of the probe by the Delaware US attorney’s office.
“I take this matter very seriously but I am confidant that a professional and objective review of this matter will demonstrate that I handled my affairs legally and appropriately, including with the benefit of professional tax advisers,” he said in a statement.
The probe raises complications for his father and whomever he selects to lead the US Department of Justice as attorney-general. Joe Biden has said he will keep the attorney-general at an arm’s length and not interfere in any individual cases.
As president, Joe Biden would have the power to issue pardons for any federal crimes.
The president-elect’s transition team said in a statement that he was “deeply proud of his son, who has fought through difficult challenges, including the vicious personal attacks of recent months, only to emerge stronger”.