The Labour leader was asked at the CBI conference whether the Queen should say sorry for making overseas investments.
He said anyone putting money into tax havens for the purposes of avoidance should "not just apologise for it, recognise what it does to our society".
The BBC has revealed that the Queen's estate has used overseas tax havens.
It comes after a leak from the tax haven of Bermuda revealed the secret overseas investments of the rich and famous, including the Queen.
Mr Corbyn's spokesman later clarified his comments, saying the Labour leader did not specifically call on the Queen to apologise but thought "anyone who puts money into a tax haven to avoid paying tax should acknowledge the damage it does to society".
Buckingham Palace has not commented on the revelation that the Duchy of Lancaster, which handles the Queen's private wealth, used offshore investments.
A spokesperson for the Duchy of Lancaster said: "We operate a number of investments and a few of these are with overseas funds. All of our investments are fully audited and legitimate.
"The Queen voluntarily pays tax on any income she receives from the Duchy."
A Downing Street spokesperson said HM Revenue and Customs (HMRC) had asked to see the leaked Paradise Papers.
Mr Corbyn called for a full inquiry, public lists of company ownership and a new tax enforcement unit to tackle tax evasion.
Theresa May said efforts were already under way to raise tax haven revenues.
Mrs May's spokesperson told reporters: "It is important to point out that holding investments offshore is not an automatic sign of wrongdoing, but HMRC has requested to see the papers urgently so it can look into any allegations."
Earlier, at the CBI conference, the prime minister did not commit to a public inquiry into tax revenue lost through offshore tax havens.
She also did not directly answer when asked whether she would insist on British overseas territories publishing a list of who owns companies and trusts they have registered.
Plans for a publicly available register were abandoned by former Prime Minister David Cameron after overseas territories lobbied against it, according to Liberal Democrat leader Sir Vince Cable.
Mrs May said HMRC had collected £160bn by tackling tax avoidance, evasion and non-compliance since 2010.
She added the UK government was working with the overseas territories "to ensure we're seeing greater transparency".
"We want people to pay the tax that is due," she said.
The premier of Bermuda said the investments were legal, and the UK bore ultimate responsibility for the rules.
On Sunday, BBC Panorama broadcast the first results of its year-long investigation into the Paradise Papers, a massive leak of financial documents from Bermuda-based law firm Appleby.
Jeremy Corbyn said the proliferation of British tax havens was "a leach on our public services by the super-rich elite".
He said the Paradise Papers were "socially damaging" and a "costly scandal" that needed to be tackled directly by the UK government.
Mr Corbyn's call for a public list of company ownership echoes an idea first mooted by former Business Secretary Sir Vince Cable.
Sir Vince criticised the government for not clamping down on offshore tax havens trading under the British flag.
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