Ms Haley, 51, and Mr Ramaswamy, 38, traded blows over foreign policy and even footwear as they joined three other 2024 candidates at the event in Miami on Wednesday night.
Donald Trump, the overwhelming frontrunner in the race, skipped the debate to hold a rival event for supporters a short drive away.
The 77-year-old former president declared the two-hour debate “unwatchable”, after it descended into an ugly row between Mr Ramaswamy and Ms Haley.
Ms Haley was later asked if she considered Mr Ramaswamy’s attacks to be “sexist”.
”I don’t even give him the time of day,” she told NBC News. “He has proven that he is just not worthy of being president of the United States.”
’A dangerous foreign policy’
“There’s so many things he said that were just uncalled for tonight,” she said, noting there were more “serious issues” to discuss.
She added: “I think he has a dangerous foreign policy that we can’t afford.”
It came after Mr Ramaswamy accused the former UN ambassador of hypocrisy over her opposition to the Chinese-owned app TikTok “while her own daughter” was using it.
”You might want to take care of your family first,” Mr Ramswamy said, to loud jeers from the audience.
A furious Ms Haley retorted: “Leave my daughter out of your voice.”
As Mr Ramaswamy continued to speak, Ms Haley shook her head and said: “You’re just scum.”
The exchange triggered a backlash from leading conservative figures.
Frank Luntz, the veteran American pollster, said that was the moment that Mr Ramaswamy lost the debate.
Dana Loesch, a conservative radio host and former spokesman for the National Rifle Association, said: “Other candidates’ kids are off-limits, no matter how desperate you are.”
Alyssa Farah, Mr Trump’s former White House communications director, said “women everywhere” would be applauding Ms Haley’s response.
As the candidate with the most polling momentum of the five on stage, Ms Haley was the focus of the majority of barbs on Wednesday night.
She was attacked over her hawkish foreign policy by Mr Ramaswamy, who compared her to George W Bush’s vice president.
The wealthy entrepreneur and political newcomer asked the audience: “Do you want a leader from a different generation who’s going to put this country first, or do you want Dick Cheney in three-inch heels?”
Ms Haley has often highlighted the fact she is the only woman in the race, and made a virtue of Mr Ramaswamy’s jibe over her footwear.
She looked askance at Mr DeSantis as she said: “They’re five-inch heels, and I don’t wear them unless you can run in them.”
Foreign policy discussion dominated the debate, the most substantive of the 2024 Republican primary contest.
While the five firmly agreed on staunchly supporting Israel, the discussion of Ukraine highlighted the party’s growing divide over continued US military support.
Ms Haley and Chris Christie, the former New Jersey governor, were alone in vociferously arguing that supporting Kyiv was in America’s national interest.
But Mr Ramaswamy, who has parroted Mr Trump’s sceptical stance towards Ukraine, questioned the wisdom of funding its war with Russia and called the country’s Jewish president, Volodymyr Zelensky, a “Nazi”.
‘He did not mean to call Zelensky a Nazi’
Mr Ramaswamy’s spokesman later said he had not meant to refer to Mr Zelensky as a Nazi.
“He was talking quickly and kind of oscillated in his words,” she said.
But it gave Ms Haley an opening to declare that Vladimir Putin and Chinese leader Xi Jinping would be “salivating” at the prospect of a candidate like Mr Ramaswamy becoming president.
With Florida governor Mr DeSantis slumping in the polls, she is now considered Mr Trump’s top challenger, albeit a distant second to the former president.
Mr Trump underscored his commanding lead as he addressed thousands of supporters in nearby Hialeah, Florida.
“Nationally, we’re up at numbers that frankly nobody’s seen before,” he said.
Speaking in a largely Hispanic area, he compared his criminal cases to the political persecution deployed by “the Cuban regime”.
Mr Trump said he did not take part in the debate because “nobody’s talking about it”.
”I’m standing in front of tens of thousands of people right now and it’s on television. That’s a hell of a lot harder to do,” he said.