The government agency said the incident on Saturday morning was part of an “ongoing situation”, but provided no further details.
The messages purported to be from the US Department of Homeland Security.
They claimed to be a warning about a supposed threat and were titled: “Urgent: Threat actor in systems.”
The emails told recipients that they were the target of a “sophisticated chain attack” from an extortion group known as the Dark Overlord, according to the non-profit anti-spam watchdog Spamhaus.
“They are causing a lot of disruption because the headers are real, they really are coming from FBI infrastructure,” Spamhaus tweeted, adding that they did not include names or contact information from the sender.
According to US media reports, more than 100,000 emails were sent out.
In a statement on Saturday, the FBI said it was “aware of the incident this morning involving fake emails from an @ic.fbi.gov email account“.
The agency said the affected hardware was quickly taken offline after the issue was detected and warned the public to be “cautious of unknown senders” and to report suspicious activity to the government.