Her medical team said she was making good progress, and were confident she would make a full recovery, said the state department.
It added in a statement that she was "eager to get back to the office".
Mrs Clinton was earlier seen leaving New York-Presbyterian Hospital with her husband and daughter.
The state department said at the time she had not been discharged, but was merely travelling to another hospital building on the campus for further tests.
The normally peripatetic and seemingly almost indefatigable Hillary Clinton hasn't been seen in public for almost a month.
What started as a stomach virus eventually led to her being admitted to hospital on Sunday, when doctors discovered a blood clot behind her right ear.
Mrs Clinton had already announced her decision to leave her post as America's top diplomat at the start of President Obama's second term in office, and senior Democrats had been urging her to run for President in 2016.
However this sudden absence from the political stage has raised questions about her health, given that she suffered a blood clot in her knee midway through her husband Bill's second term as president.
The state department says she's making good progress, but its not yet known when she'll be returning to work.
Mrs Clinton, 65, is due to stand down before President Barack Obama formally begins his second term in January.
Appointed secretary of state at the start of Mr Obama's first term, in January 2009, her health has been under intense scrutiny because she is considered a strong candidate for the Democratic nomination for president should she decide to run in 2016.
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