Senate Democrats are said to be investigating the allegation dating to the 1983-84 academic year, Mr Kavanaugh’s first at Yale University.
Deborah Ramirez, 53 – who attended Yale with Mr Kavanaugh – told The New Yorker that Mr Kavanaugh exposed himself to her during a party.
“I was embarrassed and ashamed and humiliated,” Ms Ramirez said.
In a statement issued through the White House, Mr Kavanaugh claimed that the incident “did not happen” and that it was a “smear”.
“This alleged event from 35 years ago did not happen. The people who knew me then know that this did not happen, and have said so. This is a smear, plain and simple,” Mr Kavanaugh said.