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.

The Ministry of Justice and the Wales Office said a total of £30m will also be spent on local businesses as the new £250m prison is built.
They said £1.1m had already been committed to companies in north Wales.
Work started on the prison at Wrexham industrial estate in September and is due to be completed in 2017. With 2,000 inmates it will be the UK's largest.
It is being built on the site of the former Firestone tyre factory.
The construction company Lend Lease, which has been selected to build the prison, is holding a meeting to determine how best to deliver its promises to the community during the construction.
The commitments include 100 new apprenticeships and 500 work placement days per year.

The permanent structure will replace a temporary barrier which has been in place since 2013.
Work on the trap is a collaboration between Historic Environment Scotland (HES) and the City of Edinburgh Council.
Construction will begin on Monday and is scheduled to last until March 2016. The trap consists of a wall about 3ft (1m) high, topped with metal railings.
HES director of heritage management Barbara Cummins said: "It's important that the public are assured that we have no immediate concerns regarding the rock face, however as impenetrable as the castle rock might appear, it's not immune to the effects of the weather.
"The constant freeze and thaw during the winter months can open up cracks in the rock face, which then allows a plant known as valerian to take root.
"Once this germinates the bulb expands and, over long periods of time, this process can cause rocks to fracture and fall."
There will be some traffic and parking restrictions on Johnston Terrace while the work is carried out.
Ms Cummins added: "At the moment we have a temporary structure in place which offers significant protection, and we supplement that by having our highly trained staff abseil down the rock on a regular basis to carefully remove loose fragments from the surface.
"Whilst these measures help to minimise the risk of rock falls, the regular monitoring and scaling is time consuming and ultimately disruptive to visitors to the castle and drivers on Johnston Terrace, which has to be closed whilst work is being carried out.
"The new rock trap will enhance our current risk control arrangements and reduce disruption in the process."
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.
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The "super-prison" being built in Wrexham will bring £23m a year to the local economy and 1,000 jobs.
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A new rock trap is to be constructed at Edinburgh Castle.