Mrs Clinton seemed to buckle while waiting to get into a minivan at a ceremony to mark 15 years since the 9/11 terror attacks in New York, and she needed help from her security detail.
However, in a phone interview with CNN, the Democratic candidate said she became dizzy but did not lose consciousness.
The 68-year-old said she felt immediately better after getting into her air-conditioned vehicle.
Mr Obama told a crowd in Philadelphia that Mrs Clinton had "been subjected to more scrutiny and...more unfair criticism than anybody out here".
He accused voters of giving her rival Donald Trump an easy ride, saying: "Our standards for what's normal have changed.
"Donald Trump says stuff every day that used to be considered as disqualifying for being president and, yet, because he says it over and over and over again, the press just gives up."
Meanwhile, Bill Clinton said his wife was "doing fine" and insisted "she just got dehydrated".
He told CBS: "On more than one occasion, over the last many, many years, the same sort of thing happened to her when she got severely dehydrated."
Mrs Clinton's campaign team has said it will release more of her medical records following the incident and admitted being too slow to provide information about her condition.
Mr Donald Trump has previously questioned Mrs Clinton's fitness for the presidency.
However, during a speach at a rally in Asheville, North Carolina, he was restrained on the news, saying he hoped she feels better soon.
Instead he concentrated on her remark last week that half of his supporters belonged in "a basket of deplorables".
"You cannot run for president if you have such contempt in your heart for the American voter," he said.
"You can't lead this nation if you have such a low opinion of its citizens."
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