The Rev. Paul Scalia will also deliver the homily, the sermon that explores the themes of the Bible readings at Mass, Basilica spokesman Jackie Hayes said.
President Barack Obama will travel to the Supreme Court on Friday to pay his respects to Scalia, whose death last weekend has sparked a bitter political fight.
The White House said Obama and the first lady will visit the court as Scalia's body lies in repose.
The next day, Vice President Joe Biden and his wife will attend a funeral Mass for Scalia at the Basilica.
Inside the court, Scalia's chair and the bench in front of it have been draped with black wool crepe. A black drape has also been hung over the courtroom doors.
Even amid the rancorous political battle underway over Scalia's replacement, Obama has sought to memorialize the justice, who was one of the panel's most conservative voices.
"Justice Scalia and I had different political orientations and probably would have disagreed on the outcome of certain cases. But there's no doubt that he was a giant on the Supreme Court, helped to shape the legal landscape," Obama said.
"It's important, before we rush into the all the politics of this, to take stock of somebody who made enormous contributions to the United States. And we are grateful not only for his service but for his family's service."
The REe. Paul Scalia is the delegate for priests in the Diocese of Arlington, a position he holds after three years as pastor at Saint John the Beloved Catholic Church in McLean, Virginia.
He received a Master of Arts degree from the Pontifical University of Saint Thomas Aquinas, the Angelicum, in Rome in 1996 and was ordained a priest for the Diocese of Arlington the same year.