Donald Trump's commerce secretary is shown to have a stake in a firm dealing with Russians sanctioned by the US.
The leak, dubbed the Paradise Papers, contains 13.4m documents, mostly from one leading firm in offshore finance.
BBC Panorama is part of nearly 100 media groups investigating the papers.
As with last year's Panama Papers leak, the documents were obtained by the German newspaper Süddeutsche Zeitung, which called in the International Consortium of Investigative Journalists (ICIJ) to oversee the investigation. The Guardian is among the nearly 100 media partners involved in investigating the documents.
Sunday's revelations form only a small part of a week of disclosures that will expose the tax and financial affairs of some of the hundreds of people and companies named in the data, some with strong UK connections.
Many of the stories focus on how politicians, multinationals, celebrities and high-net-worth individuals use complex structures of trusts, foundations and shell companies to protect their cash from tax officials or hide their dealings behind a veil of secrecy.
The vast majority of the transactions involve no legal wrongdoing.
The Paradise Papers show that about £10m ($NZ24.6m) of the Queen's private money was invested offshore.
It was put into funds in the Cayman Islands and Bermuda by the Duchy of Lancaster, which provides the Queen with an income and handles investments for her £500m private estate.
There is nothing illegal in the investments and no suggestion that the Queen is not paying tax, but questions may be asked about whether the monarch should be investing offshore.
There were small investments in the rent-to-buy retailer BrightHouse, which has been accused of exploiting the poor, and the Threshers chain of off-licences, which later went bust owing £17.5m in tax and costing almost 6,000 people their jobs.
The Duchy said it was not involved in decisions made by funds and there is no suggestion the Queen had any knowledge of the specific investments made on her behalf.
The Duchy has in the past said it gives "ongoing consideration regarding any of its acts or omissions that could adversely impact the reputation" of the Queen, who it says takes "a keen interest" in the estate.
Photo: AFP Caption: The leaks show about £10m of the Queen's private money was invested offshore.