Ginsburg died on Friday of metastatic pancreatic cancer at her home in Washington, DC, surrounded by her family, the statement said.
Earlier this year, Ginsburg said she was undergoing chemotherapy for a recurrence of cancer.
She was a prominent feminist who became a figurehead for liberals in the US.
Ginsburg was the oldest justice and the second ever woman to sit on the Supreme Court, where she served for 27 years.
"Our Nation has lost a jurist of historic stature," Chief Justice John Roberts said in a statement on Friday. "We at the Supreme Court have lost a cherished colleague. Today we mourn, but with confidence that future generations will remember Ruth Bader Ginsburg as we knew her - a tireless and resolute champion of justice."