Hillary Clinton received at least five emails containing malware.
The “phishing” emails, disguised as speeding tickets, would have enabled the hackers to control her computer.
The infected computer would have sent information to at least three computers overseas, including one in Russia.
A spokesman for HillaryClinton said there was no evidence of a breach.
The hacking attempts were included in thousands of emails released by the State Department.
Hillary Clinton’s opponents have accused her of putting US security at risk by using an unsecured computer system.
The Democrat presidential hopeful says no classified information was sent or received.
The five emails, sent over a four-hour period in August 2011, show hackers had Hillary Clinton’s email address, which was not public, and contained a virus concealed as a speeding ticket from New York state, where she lives.
The email containing instructions to open and print the speeding ticket misspelled the name of the city concerned, Chatham, came from a supposed New York City government account and contained a “Ticket.zip” file of the kind usually picked up by commercial antivirus software.
Nick Merrill, a spokesman for Hillary Clinton’s presidential campaign, said there was no evidence to suggest she replied to the emails or opened the attachment.
“All these emails show is that, like millions of other Americans, she received spam,” he said.
The state department disclosed that Hillary Clinton used a private server during her time as secretary of state (between 2009 and 2013) after journalists requested copies of her government emails.
Hillary Clinton has admitted that her decision to use a private email server at her New York home was a mistake.
However, the latest set of her emails to be released also reveal frustration within the State Department at the technology it was using while she was in office.
In one email exchange Hillary Clinton’s then head of policy Anne-Marie Slaughter wrote that the department’s technology was “so antiquated” that high-level officials “routinely end up using their home email accounts to be able to get their work done quickly and effectively”.
Anne-Marie Slaughter suggested writing an opinion piece to highlight the problem and Hillary Clinton agreed the idea “made good sense”, but her chief of staff Cheryl Mills warned against “telegraphing” how often senior officials relied on their private email accounts to do government business because it could encourage hackers.
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