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 of confidential papers from Bermuda revealed the secret offshore 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".
Mr Corbyn called for a full inquiry, public lists of company ownership, and a new tax enforcement unit to tackle tax evasion.
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.
The leaks raised questions over tech firm Apple's tax structures, the investments of Conservative Party donor Lord Ashcroft, Everton FC owner Farhad Moshiri, Formula 1 champion Lewis Hamilton, and offshore investments made on the Queen's behalf by the Duchy of Lancaster.
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."
HMRC chief executive Jon Thompson vowed to "chase down" anyone trying to hide money offshore and evade tax.
He told the Commons Public Accounts Committee that HMRC had asked to see the leaked Paradise Papers in order to "look at every case of tax evasion very seriously".
Mr Thompson said there were 66 ongoing criminal investigations into the Panama Papers, which in April 2016 exposed tax avoidance and evasion, saying £100m could be retrieved.
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