Sir Philip Green has said it was “outrageous” for Lord Hain to name him as the man who prevented the Telegraph publishing allegations of sexual and racial harassment.
He said the Labour peer had also failed to disclose his financial links to the law firm representing the newspaper.
Sir Philip has denied the allegations and said he would lodge a formal complaint with the House of Lords.
Lord Hain insisted naming the retail tycoon was in the public interest.
In a statement Sir Philip said he had been advised that Lord Hain’s actions are likely to have breached the House of Lords Code of Conduct.
The Daily Telegraph first reported on the injunction on Wednesday, saying a “leading businessman” had won a legal battle to stop the newspaper printing “confidential information” from five employees.
Lord Hain identified the Topshop boss in the Lords on Thursday using parliamentary privilege, which protects MPs and peers from being prosecuted for libel over statements made in the Houses of Parliament.
It has since emerged the peer is a global and government adviser at Gordon Dadds, the law firm used by the Telegraph.
In a statement, Gordon Dadds said Lord Hain had not obtained any information from it regarding the case, “including any information which would enable him to identify Philip Green as having any involvement in it”.
Lord Hain has “categorically” denied that he was aware of the law firm’s work with the Telegraph and said the firm played “absolutely no part” in his decision to name Sir Philip.
The Telegraph says it spent eight months investigating allegations of bullying, intimidation and sexual harassment against Sir Philip.
After he was contacted for a comment in July, Sir Philip and a number of senior staff applied for an injunction to stop details being published, the Telegraph said.
A High Court judge refused to grant the gagging order the following month, but Appeal Court judges ruled in Sir Philip’s favour on Tuesday.
The BBC has not been able to verify the allegations contained in the Telegraph’s report.
Sir Philip has “categorically and wholly” denied allegations of “unlawful sexual or racist behaviour”.