The investigation is being conducted by federal prosecutors in Delaware. US media quote sources saying it relates to business dealings with foreign countries including China.
Hunter Biden said he was confident he would be shown to have done no wrong.
The Biden-Harris transition team said the president-elect was “deeply proud of his son”.
A statement from the team said Hunter had “fought through difficult challenges, including the vicious personal attacks of recent months, only to emerge stronger”.
The 50-year-old said he had learned of the investigation on Tuesday. He did not disclose any further details.
“I take this matter very seriously but I am confident that a professional and objective review of these matters will demonstrate that I handled my affairs legally and appropriately, including with the benefit of professional tax advisers,” he said.
Reports say the investigation was begun in 2018, before Joe Biden announced his bid for the presidency.
Hunter Biden was a frequent target of Republican criticism during the 2020 election campaign, focusing on his business dealings in Ukraine and China when Joe Biden was vice-president in the Barack Obama administration.
Last December, President Donald Trump was impeached by the Democratic-run House of Representatives on charges of abuse of power and obstruction of Congress stemming from his attempts to pressure Ukraine to investigate the Bidens.
But Mr Trump was cleared by the Republican-held Senate in February.
The new investigation into Hunter Biden’s tax affairs comes as his father assembles his cabinet. If the case is still ongoing when Mr Biden is sworn into office next month, his pick for attorney general could have oversight of the investigation, AP notes.
The presidential election is over, but it seems President-elect Joe Biden’s son Hunter – a regular target of Republican attacks during the campaign – is going to stay in the news.
The revelation that Hunter is under tax investigation is not entirely surprising. There have been hints of such an inquiry for months. With official confirmation, however, comes further scrutiny – and potential political headaches for the president-elect. -BBC