Brooks, 45, who later became chief executive of the British newspaper arm of News Corp, also said she did not know phone-hacking was illegal while she was the paper's editor.
The revelation in 2011 that Dowler's phone had been intercepted by the tabloid while the 13-year-old was missing led to widespread public condemnation that caused Murdoch to shut the 168-year-old paper and forced Brooks to resign.
Asked whether she had anything to do with a journalist tasking private detective Glenn Mulcaire to hack Dowler's phone, she said: "No I didn't", adding she first learned the News of the World had hacked the phone on July 4, 2011, just days before the paper was shut and she was arrested.
Her reaction to the news was "shock, horror", she said.
The fallout from the Dowler hacking revelation rocked not just Murdoch's media empire but the British establishment, and led to Prime Minister David Cameron, a close friend of Brooks, launching an inquiry into press ethics.
Brooks denies conspiracy to intercept voicemail messages on mobile phones, authorising illegal payments to public officials and conspiracy to pervert the course of justice.
Giving evidence for a third day at the Old Bailey court, she told the jury she had never given approval for anyone to access voicemails.
She said she had learned phone-hacking was possible in the late 1990s but had not realised it was a criminal offence.
"I don't think anybody, me included, knew it was illegal," she said.
Despite this, she said privacy concerns would have prevented her from using phone-hacking to get stories. She said she would only have contemplated giving approval in very serious cases, citing a story about an arms dealer by a reporter on a rival paper who had used the practice.
She told the court that during her time as editor she did not think phone-hacking would have been particularly useful.
"I suppose the showbiz department if it was looking for tittle-tattle (it) could be," she said.
The court has heard that the hacking of Dowler's phone occurred while Brooks was on holiday in Dubai when she was in regular contact with the paper and her deputy Andy Coulson
Asked by her lawyer Jonathan Laidlaw if she had learned about Dowler's phone being intercepted while she was away, she replied: "Absolutely not".
"I don't remember having any discussion about her disappearance while I was away."
She also denied knowing about a later discussion between the paper and the police searching for the missing girl in which it was disclosed they had heard Dowler's voicemails.
Earlier Brooks told the court she had never heard Mulcaire's name before his arrest for phone-hacking offences in 2006 and had not seen the £92,000 pound a year contract awarded by the tabloid him in September 2001.
