Physician Lisa Bardack examined the 68-year-old Clinton at her home in Chappaqua, New York, after she was forced to leave the ceremony at Ground Zero, a campaign aide said.
Video footage showed the candidate stumble as she was helped into her vehicle, and she needed to be held up on both sides by members of her entourage.
"Secretary Clinton has been experiencing a cough related to allergies. On Friday, during follow-up evaluation of her prolonged cough, she was diagnosed with pneumonia," Bardack said in a statement released by Clinton's campaign.
"She was put on antibiotics, and advised to rest and modify her schedule. While at this morning's event, she became overheated and dehydrated. I have just examined her and she is now re-hydrated and recovering nicely."
ANOTHER ANGLE OF #CLINTONCOLLAPSE WOW. pic.twitter.com/jqOpP11omI — Stefan Molyneux (@StefanMolyneux) September 11, 2016
The former secretary of state was at the high-profile ceremony at Ground Zero in Manhattan for 90 minutes and greeted some family members of those killed in the deadly terror strikes 15 years ago, her campaign said in a statement.
"During the ceremony, she felt overheated so departed to go to her daughter's apartment, and is feeling much better," the statement said.
An AFP journalist at the ceremony noted that Clinton, dressed in a navy suit and white blouse, was greeting people as she left and did not appear to be rushing out. She walked out accompanied by an aide at her elbow.
However, a video posted on Twitter showed Clinton seeming unsteady as she waited to get into a black van. She appeared to stumble as she was helped into the vehicle, held up on either side by members of her entourage.
It was a humid day in New York, with temperatures around 82 degrees Fahrenheit (28 Celsius).
Clinton reappeared a few hours later, apparently recovered as she walked out of her daughter Chelsea's home. She smiled for the media and posed for pictures with a young girl before departing in a vehicle for her home in Chappaqua.
"I'm feeling great, it's a beautiful day in New York," Clinton said.
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Health issues?
Trump was uncharacteristically silent on Twitter after Clinton's illness, as both candidates took a break from formal campaigning to mark the somber day of remembrance in the United States.
But the businessman, his spokespeople and surrogates have promoted the idea in recent weeks that Clinton, 68, has serious health problems.
The internet is awash with claims that she may have a brain tumor, Parkinson's or dementia. Some complain that she has "seizure-like facial expressions" and others allege that she twitches.
Trump, 70, has said Clinton is "not strong enough to be president" and that she "lacks the mental and physical stamina to take on ISIS."
Former New York mayor Rudy Giuliani, a Trump supporter, has said that Clinton was "tired" and "looked sick."
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Trump spokeswoman Katrina Pierson, who is not a doctor, last month diagnosed Clinton with dysphasia, a disorder that impairs speech and comprehension.
The root of the claims lies in 2012, when Clinton was nearing the end of her stint as secretary of state and a stomach virus and dehydration prompted her to faint, causing what her doctor said was a concussion.
They said they found a blood clot on the brain and Clinton complained of double vision. She appeared in spectacles featuring a prism when testifying before Congress on Benghazi in January 2013. She was later given the all-clear.
"What the Clinton campaign needs to do over the course of the next several days is demonstrate her vitality and viability. She has to be at tons of events and seem very energetic."
The former first lady has dismissed "conspiracy theories" about her health and points to a detailed report from her doctor declaring her fit to serve as president.
She blamed a coughing fit during a speech in Cleveland last week on allergies.
'Vitality and viability'
Clinton's sudden illness is unlikely to be a turning point in the White House race, said Jennifer Lawless, a professor of government at American University in Washington.
From all indications, it appears to just be a brief bout of overheating, she told AFP.
"What the Clinton campaign needs to do over the course of the next several days is demonstrate her vitality and viability. She has to be at tons of events and seem very energetic," Lawless said.
Clinton had been trying to move on from a blunder in which she told a crowd at a fundraiser late Friday that "to be grossly generalistic, you could put half of Trump's supporters into what I call the basket of deplorables."
"The racist, sexist, homophobic, xenophobic, Islamophobic -- you name it."
Trump and his supporters slammed the remarks. Clinton said she regretted saying "half," but then listed a number of "deplorable" things about Trump.
"I won't stop calling out bigotry and racist rhetoric in this campaign," she said.
A Washington Post-ABC News poll out Sunday -- conducted in the days before she made the remark -- shows that 70 percent of the electorate has already decided who to vote for, and only 30 percent are undecided or could switch.
Clinton leads Trump 46 percent to 41 percent lead among likely voters, according to the poll, which had a 4.5 percentage-point margin of error.
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