Justice Ginsburg, 80, officiates this weekend at the wedding of Michael Kaiser, 59, president of the Kennedy Center performing arts space, and economist John Roberts, 32.
Mr Kaiser is a personal friend of hers.
In June, the Supreme Court overturned a law that banned recognition of same-sex marriages by the US government.
The ruling granted legally married gay men and women access to the same federal entitlements available to opposite-sex married couples.
Justice Ginsburg, who was appointed to the nine-member high court in 1993 by President Bill Clinton, voted in the majority in that case.
Same-sex marriage is now legal in 13 states and Washington DC, and since the court's decision, the federal government under President Barack Obama has taken several steps to grant same-sex marriage couples the same legal status as opposite-sex couples.
The ceremony will take place at the Kennedy Center in Washington, the Associated Press reports.
Justice Ginsburg told the Washington Post newspaper she believed none of the Supreme Court justices had been asked previously to conduct a same-sex ceremony for fear it would compromise their ability to hear a case on the issue.
US Supreme Court Justice Ruth Bader Ginsburg is poised to become the first judge on the country's highest court to perform a same-sex marriage.