The Supreme Court said in a statement that Ginsburg died at home.
The Ginsburgs celebrated their 56th wedding anniversary last week. They met on a blind date as undergraduates at Cornell University.
Martin Ginsburg was an expert in tax law and taught at New York University, Columbia University and Georgetown University over the course of his career.
Judy Areen, interim dean of Georgetown University Law Center, said Sunday: "Marty Ginsburg was not only one of the most innovative legal thinkers of our time, he was a gifted teacher and respected colleague. He will be deeply missed."
Survivors also include two children, Jane and James.
A private burial will take place at Arlington National Cemetery.