It is alleged that the Duchy of Lancaster, which handles the Queen's investments, has held funds in the Cayman Islands and Bermuda.
Around GBP10 million ($NZ22m) of the Queen's private cash is said to have been tied up in offshore portfolios, the BBC reports.
There is nothing to suggest that any investments are illegal.
The documents show that Commerce Secretary Wilbur Ross, the Trump administration's point man on trade and manufacturing policy, has a stake in a company that does business with a gas producer partly owned by the son-in-law of Russian President Vladimir Putin.
According to the ICIJ, Ross is an investor in Navigator Holdings, a shipping giant that counts Russian gas and petrochemical producer Sibur among its major customers. Putin's son-in-law Kirill Shamalov once owned more than 20 per cent of the company, but now holds a much smaller stake.
Commerce Department spokesman James Rockas said Ross "never met" Shamalov and has generally supported the Trump administration's sanctions against Russia, according to the ICIJ report.
The German newspaper, which began reporting on the content of the documents late on Sunday, said they show how big companies and the super wealthy hide their money using tax havens.
Sueddeutsche Zeitung and ICIJ said the bulk of the documents were from the prestigious offshore law firm Appleby, which was founded in Bermuda and has offices in several other locations.
ICIJ said clients include financial institutions, such as Citigroup and Bank of America, as well as technology giants Apple and Uber, and brands like Nike.
Appleby calls itself "one of the world's largest providers of offshore legal services", and admitted last month that it had been hacked.
The cache of documents also includes half a million records from Asiaciti Trust, a firm based in Singapore that specialises in off-shore services for clients.