Bosses issued a denial after Grant had told the Leveson Inquiry of his suspicions about a story published four years ago.
A spokesman for the newspaper said information had come from a freelance journalist who had spoken to a “source”.
Grant told Lord Justice Leveson about the “bizarre, left field” story and said that he would “love to hear the [Mail on Sunday’s] explanation”.
He said he had not made the allegation in public before but said he had been preparing documents and going through his “trials and tribulations” when the “penny dropped”.
Grant said that the story claimed that his relationship with then girlfriend Jemima Khan was on the rocks because of his “late night phone calls with a plummy-voiced studio executive”.
He said the story was untrue and he had not been able to think “for the life of me” what the source of the story could be.
The only explanation he could think of was that messages had been left on his phone by an executive’s assistant, who had a voice which could be described as “plummy”.
The paper’s spokesman said: “The Mail on Sunday utterly refutes Hugh Grant’s claim that they got any story as a result of phone hacking.
“In fact in the case of the story Mr Grant refers to, the information came from a freelance journalist who had been told by a source who was regularly speaking to Jemima Khan.”
In April 2007, Grant accepted undisclosed libel damages over claims that his relationship with Khan was destroyed by a flirtation with a film executive — and his conduct over Liz Hurley’s wedding.
The settlement of Grant’s legal actions over articles in the Mail on Sunday and the Daily Mail in February 2007 was announced at the High Court in London.
Grant’s solicitor said the damages would be donated to the Marie Curie Cancer Care charity.
He said the first article — Hugh, Drew and the Jealousy of Jemima — alleged that Grant, while in a relationship with Khan, was conducting a flirtation with a female senior Warner Bros executive.
Smith said that Grant did not know of a woman from Warner Bros matching this description, let alone that he was conducting a flirtation with her. As far as he was aware, she simply did not exist.
After that hearing, Grant said: “I took this action because I was tired of the Daily Mail and Mail on Sunday papers publishing almost entirely fictional articles about my private life for their own financial gain.
“I’m also hoping that this statement in court might remind people that the so-called ‘close friends’ or ‘close sources’ on which these stories claim to be based almost never exist.”
Grant said journalists were “entitled to their opinion” but hit out at “lazy reporting”.
The actor said he did not want to see the end of popular print journalism and sought to protect the British instinct to be “sceptical, irreverent, difficult and to take the piss”.
But he went on: “There has been a section of our press that has been allowed to become toxic over the last 20 or 30 years, its main tactic being bullying and intimidation and blackmail.
“I think that that needs a lot of courage to stand up to, and I think this country’s had a historically good record standing up to bullies. I think it’s time this country found the courage to stand up to this bully now,” the actor added.
Meanwhile private detective Glenn Mulcaire last night denied deleting messages from Milly Dowler’s phone as the murdered schoolgirl’s parents spoke of their agony over the hacking scandal.
The investigator is accused of illegally accessing the teenager’s voicemails after she went missing in 2002 but his solicitor said he had “no reason” to erase any of them.
Milly’s mother Sally told the Leveson Inquiry that she did not sleep for three nights after police told her Mulcaire had hacked her daughter’s phone.
The private detective’s solicitor, Sarah Webb, said Mulcaire had expressed his “sincere personal sympathy’ for the Dowlers but could not say much because of the ongoing police investigation into hacking.
“He confirms that he did not delete messages and had no reason to do so,” she added. Sally Dowler told the inquiry of her and her husband Bob’s joy when they were given false hope that Milly was still alive after someone — identified at the hearing as Mulcaire — deleted voicemails.
She rang her 13-year-old daughter’s mobile phone repeatedly in the weeks after she vanished, leaving messages for her until the mailbox became full and it switched to a recording.
Dowler kept calling Milly’s number and felt elation when she got through to her recorded greeting.
She told the inquiry: “I rang her phone. It clicked through onto her voicemail, so I heard her voice and it was just like, ‘she’s picked up her voicemail, Bob, she’s alive!’ “When we were told about the hacking, that’s the first thing I thought.”
Sally Dowler described the moment, just before the start of the trial of the serial killer accused of Milly’s murder, when police told her and her husband that Mulcaire was commissioned by the News of the World to hack their daughter’s phone.
“As soon as I was told it was about phone hacking, literally I didn’t sleep for about three nights because you replay everything in your mind and just think, ‘oh, that makes sense now, that makes sense’,” she said.
Mulcaire was jailed along with the News of the World’s former royal editor Clive Goodman in January 2007 after they admitted to intercepting voicemail messages left on phones belonging to royal aides.
Prime Minister David Cameron set up the Leveson Inquiry in July in response to the revelation that the News of the World commissioned Mulcaire to hack Milly’s phone.
The first part of the inquiry is looking at the culture, practices and ethics of the press in general.
The second part, looking at the extent of unlawful activities by journalists, will not begin until detectives have completed their investigation and prosecutions have concluded.