During dramatic testimony at the trial of two of Murdoch's former editors, a shocked Law was passed a note with the name of a close family member he was told was selling details to the paper at the time it printed stories about his ex-girlfriend Sienna Miller and her affair with James Bond actor Daniel Craig.
Asked when he had first learned of this suggestion, Law, whose voice cracked slightly, told the packed courtroom: "Today. I wasn't aware of that."
Law, 41, is the most high-profile figure to give evidence at the trial, which began at the end of October last year, of Andy Coulson and Rebekah Brooks, former editors of the News of the World. They deny charges relating to phone-hacking.
"You are probably the first witness who I don't need to ask who you are or what you do," prosecutor Andrew Edis told him.
The jury was told that personal details relating to Law and those close to him had been found on notebooks at the home of Glenn Mulcaire, a private investigator for the News of the World who has admitted phone-hacking charges.
The numbers included the cell phone for his ex-agent in Los Angeles and of mobiles he had been loaned by film companies while working on movies such as "Cold Mountain" in the United States from 2003 to 2005.
He confirmed that recordings of voicemail messages he had left for his nanny were also found at Mulcaire's home.
Law said photographers used to hound him and that the press had "an unhealthy amount" of information about his private life.
"I became aware I was turning up at places having arranged to go there secretly and the media would already be there," said the actor, who is currently appearing on stage in London's West End in a production of Shakespeare's "Henry V".
Smartly dressed in a grey suit, Law said press interest in his private life had increased significantly after he was nominated for an Oscar for "The Talented Mr Ripley" in 2001 and split from his then wife Sadie Frost.
The attention continued and grew when he began a relationship with "Layer Cake" actress Miller.
007 ACTOR'S AFFAIR
The disclosure about his unnamed relative came during cross-examination over the sourcing for a story in October 2005 revealing an affair between Craig and Miller, and how Law had telephoned the British 007 actor to confront him about it.
"We had known each other many, many years. The conversation took on all sorts of turns," Law said of the call.
Timothy Langdale, the lawyer for Coulson, the editor at the time and later Prime Minister David Cameron's media chief, asked Law if he was aware an immediate family member had been talking to the paper and had been paid.
The surprised-looking actor said he only found out about the contact late last year and knew nothing about money changing hands.
He was also passed notes with the names of a former publicist and an ex-employee, which were also not read out, whom Langdale said had been in contact with the tabloid.
Asked by the prosecution if he had had any involvement in the story about his phone call to Craig ending up in the paper, Law replied: "No. I would have been perfectly happy if that had never appeared."
Coulson and Brooks are on trial accused of conspiring to illegally intercept voicemail messages on mobile phones.
They are also accused of authorising illegal payments to public officials while Brooks faces charges of perverting the course of justice by attempting to conceal evidence from police.
They and five others deny all the charges.
