The allegation about the practice has been made by the American Civil Liberties Union (ACLU), which says it is illegal, and has therefore decided to make a complaint to the US Equal Employment Opportunity Commission.
The complaint centres on three specific incidents involving women in the states of Ohio, Pennsylvania and Illinois, where the job-seekers were not shown ads for what have typically been male-dominated industries.
Galen Sherwin, from the ACLU's Women's Rights Project, explained: "When employers in male-dominated fields advertise their jobs only to men, it prevents women from breaking into those fields.
"What's more, clicking on the Facebook ads brought viewers to a page listing numerous other job opportunities at these companies for which job seekers might be qualified.
"Because no women saw these ads, they were shut out of learning not only about the jobs highlighted in the ads, but also about any of these other opportunities."
In response to the allegation, Facebook has revealed it is looking forward to defending its practices.
Joe Osborne, a spokesperson for the company, explained: "There is no place for discrimination on Facebook.
"It's strictly prohibited in our policies, and over the past year, we've strengthened our systems to further protect against misuse."