Papers seen by the BBC's Panorama show she was a director of Bahamian firms Advanced Asset Allocation Fund and Advanced Asset Allocation Management between 1998 and 2000.
Home Secretary Amber Rudd used to be a director of two offshore companies, leaked documents reveal.
Ms Rudd, who became an MP in 2010, has not responded to questions about the firms and the role she played in them.
But there is no suggestion she herself used the companies to avoid tax.
The Bahamas has been criticised for holding out against international attempts to improve transparency and crack down on tax evasion and avoidance. Last year the European Union listed the Bahamas among 30 unco-operative tax havens.
Earlier this year, Ms Rudd - who was appointed home secretary by Theresa May when she became prime minister - defended David Cameron over his investment in an offshore fund set up by his late father in the Bahamas.
Ms Rudd did not mention her own experience of offshore investment funds, but stressed that "international transparency on tax matters is essential."
Her directorships were discovered among details of more than 176,000 companies set up in the Caribbean tax haven that have been leaked to the media.
According to a former business associate of hers, the companies were involved in an offshore investment fund.
Alistair Buchanan, who marketed the fund to investors, said the fund was set up in the Bahamas for regulatory reasons, rather than tax reasons.
"You could not set up those funds in England at that time, now you can," he said.
The fund was licensed by the Bahamas Securities Commission and the registered agent was Citco Fund Services (Bahamas) Limited.
Citco is an international company that runs services for hedge funds, private equity, real estate and fund investments. Citco declined to comment about the offshore fund.
In 1999, Ms Rudd was appointed a director of Mr Buchanan's own UK company, Seaforth International Limited.
Mr Buchanan said Seaforth was working with funds and finding investors.
"It was a combination. We worked with family offices, high net worth private clients, funds of funds, and private investors introduced by intermediaries. And Amber, at that point, was a close friend.
"I wanted her assistance and knowledge in setting up my own show. That's why she ended up being a director."
Following the revelations, Green Party speaker on finance Molly Scott Cato MEP commented: "Theresa May made clear that she would lead a government that works for everyone and would encourage a more ethical approach to business.
"In this context it is difficult to see how she can continue to have confidence in Amber Rudd as home secretary."
And Liberal Democrat leader Tim Farron tweeted that Ms Rudd "must provide clarity".
A spokesperson for the home secretary, meanwhile, told the Guardian: "It is a matter of public record that Amber had a career in business before entering politics."
The leaked files from the company registry in the Bahamas contain basic information about offshore companies, trusts and foundations registered on the islands.
They include names of directors, company administrators and other corporate documentation for entities incorporated between 1990 and 2016.
The 1.3 million files were obtained by the German newspaper Sueddeutsche Zeitung and shared with the International Consortium of Investigative Journalists (ICIJ) and media partners including BBC Panorama and the Guardian.
The ICIJ plans to combine the new Bahamas data with information from previous offshore leaks - including the Panama Papers - to create the largest public registry of offshore entities in history.