Deborah Ramirez has alleged that Mr Kavanaugh exposed his genitals to her at a party in the 1980s.
They were both students at the time when the act allegedly took place in New Haven, Connecticut.
According to her lawyer, she has agreed to cooperate with the investigation.
Three women have now accused Brett Kavanaugh of sexual misconduct.
One of them, Dr Christine Blasey Ford, testified before the Senate Judiciary Committee last week.
US President Donald Trump instructed the FBI to reopen its investigation following a plea from Republican Senator Jeff Flake.
According to NBC News reports, limits have been placed on the investigation by the White House so that a third woman, Julie Swetnick, would not be questioned.
Despite growing criticism surrounding the President’s involvement in the process, US administration officials have stated it is not unusual for the White House to be involved when it concerns a presidential nominee.
Both Mr Kavanaugh and Dr Ford testified at a Senate hearing on Thursday.
Ms Ford stated that Mr Kavanaugh and one of his friends attacked her at a house party in 1982 in Maryland.
Mr Kavanaugh followed Ms Ford’s testimony in angry fashion, berating Democrats and accusing them of a politically motivated attack.
Protestors confronted prominent Republican Senator Jeff Flake on Friday before he voiced support for the FBI to reopen their investigation into Mr Kavanaugh.
However, he still voted to send the nomination to the Senate floor, and a vote is expected to take place after the investigation is concluded by Friday 5 October.
Julie Swetnick, a third accuser, came forward on Wednesday and said in a statement: “In approximately 1982, I became the victim of one of these gang or train rapes where Mark Judge and Brett Kavanaugh were present.”
However, it was not clear whether they actually took part in the act.
Mr Judge has strongly denied these allegations.