The doctor`s statement said she was now re-hydrated and "recovering nicely".
But a campaign official said she has cancelled a campaign trip to California due to the illness.
She was due to leave for California on Monday morning for a two-day trip that included fundraisers and a speech on the economy.
"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," Dr Bardack`s statement said.
"She was put on antibiotics, and advised to rest and modify her schedule," it went on.
On Sunday, video showed her being supported by aides as they put her into her van after she left the 9/11 ceremony in New York early.
Her Republican opponents have queried her physical fitness, with the presidential candidate Donald Trump telling supporters last month she "lacks the mental and physical stamina" to serve as president and fight Islamic State militants.
Last month Dr Bardack said she was "in excellent health and fit to serve as president of the United States".
She made a full recovery from surgery she underwent in 2012 for a blood clot, the doctor said.
The Clinton campaign has accused opponents of pushing a "deranged conspiracy about Clinton`s health".
Mrs Clinton is 68. Her Republican opponent Donald Trump is 70.
Emerging later on Sunday from her daughter`s home in New York, Mrs Clinton had said: "I`m feeling great. It`s a beautiful day in New York."
She then left for her home in Chappaqua, New York, and on Sunday evening Dr Bardack issued the health update.
Earlier on Sunday, the Clinton campaign had responded to news of the incident at the ceremony by saying she had "felt overheated".
The candidate came to the ceremony fresh from a political storm over comments she made about Mr Trump`s supporters at a fundraiser on Friday.
She had apologised on Saturday for suggesting half of the Republican`s supporters were "deplorables".
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