FBI Director James Comey informed Congress of the move in a letter on Friday, 11 days before the election.
Mrs Clinton told supporters the move was "unprecedented" and "deeply troubling".
But Republican opponent Donald Trump has praised the bureau's decision.
In his letter to Congress, Mr Comey said the FBI had learned of fresh emails which might be "pertinent" to its previous inquiry into the Democratic candidate's use of a private server when she was secretary of state in the Obama administration.
Mr Comey has defended the move, insisting that not making it public would be "misleading" and also risked being "misunderstood", given that the FBI does not know the significance of the newly found emails.
Speaking to supporters in Florida on Saturday, Mrs Clinton said: "It's not just strange, it's unprecedented. And it is deeply troubling because voters deserve to get full and complete facts.
"So we've called on Director Comey to explain everything right away, put it all out on the table."
Mrs Clinton has said she is confident the investigation into the emails will not change the FBI's original finding in July, which criticised her but cleared her of any illegal acts.
Mr Comey has been heavily criticised by Clinton supporters - and according to the New York Times, justice department officials - for his decision to make the information public so close to polling day.
In a memo he acknowledged "we do not ordinarily tell Congress about ongoing investigations". But he said he felt an "obligation" to do so given that he had previously testified that the FBI investigation was complete.
Clinton campaign chairman John Podesta said the information provided by Mr Comey was "long on innuendo" and "short on facts".
There was, he said, "no evidence of wrongdoing. No charge of wrongdoing. No indication this is even about Hillary".
Mr Trump meanwhile has said the issue is the biggest political scandal in the US since Watergate, which brought down President Richard Nixon.
At a rally in Colorado on Saturday, he said: "Her criminal action was wilful, deliberate, intentional and purposeful.
"Hillary set up an illegal server for the obvious purpose of shielding her illegal actions from public disclosure and exposure."
The FBI has already established that Mrs Clinton had held classified information on a private email server.
In July, Mr Comey said Mrs Clinton's handling of sensitive material during her tenure as secretary of state was "extremely careless", but cleared her of any criminal wrongdoing.
The latest emails were discovered as part of a separate investigation into the estranged husband of top Clinton aide, Huma Abedin.
Devices belonging to her and Anthony Weiner, a former high-flying congressman, were seized in an investigation into whether he sent sexually explicit emails to a 15-year-old girl in North Carolina.
Investigators are reviewing the documents to see if they contain classified information.
The former secretary of state's private email server was first revealed in March 2015 by the New York Times.
She did not immediately express regret, and said the main reason for her "email@example.com" address was "convenience".
Soon after that she apologised in an interview with ABC News, and has since said sorry to voters a number of times.