Lord Justice Leveson summoned Fawkes, real name Paul Staines, to appear before the inquiry to explain how a document purporting to be evidence of Tony Blair's former communications chief Alistair Campbell could have been released on his Order-order blog three days before it was due to be heard.
The document is said to contain evidence from Campbell that a newspaper had hacked his phone, as well as intercepted the voicemail messages of the then prime minister's wife Cherie Blair while they were living at Number 10.
Staines, who is due to appear before Lord Leveson this week, claims that he obtained the papers legally.
But Campbell, a former Daily Mirror journalist, said that he was "extremely concerned" to hear that his evidence was already in the public domain.
In a statement published on its official website, the inquiry said: "The website (Order-order) asserts that this statement was obtained by 'legal means' but Lord Justice Leveson will be enquiring further into this claim and Mr Paul Staines will be required to give evidence pursuant to s21 of the Inquiries Act 2005.
"Witness statements are disclosed under strict confidentiality agreements in order that participants can prepare for the evidence; that confidentiality must be observed to maintain the integrity of the Inquiry."
Campbell's statement will now be published today on the inquiry website, rather than immediately after he gives evidence in person on Wednesday, as per usual procedure.
Staines's website published extracts from what it claimed was Campbell's evidence, alongside a link to the full document. It is not clear whether this was the final document, or an earlier draft of the statement.
The blogger highlighted various potentially contentious elements in the evidence, including a string of damaging claims against the newspapers.
The most notable allegation was that Cherie Blair's mobile phone may have been hacked, although Campbell admitted that he had no evidence to back up this claim.
The landlord wrongly accused of Joanna Yeates's murder, the singer Charlotte Church and former TV presenter Anne Diamond are amongst those due to give evidence today at the inquiry.
Leveson Inquiry coverage roundup:
> JK Rowling criticises 'threatening' press treatment
> Harry Potter newspaper articles criticised by JK Rowling
> Sienna Miller 'baffled and intimidated' by press intrusion
> Madeleine McCann parents Kate and Gerry 'violated' by press intrusion
> Phone hacking goes beyond News of the World, says lawyer
> Steve Coogan: Newspaper industry is like the mafia
> Phone hacking made Dowler family think Milly was alive
> Hugh Grant suspects Mail On Sunday of phone hacking