His daughter said the cause was complications from pneumonia, the Post reported.
Schlesinger served as defense secretary for Presidents Richard Nixon and Gerald Ford and was the nation's first energy secretary under President Jimmy Carter.
The Center for Strategic and International Studies, where Schlesinger had been a trustee for more than 30 years, posted a message on its website that said: "He left an astounding mark on American security and energy policy. After leaving government, Dr. Schlesinger continued to promote a stronger and more prosperous country through his work at many policy institutions, including CSIS. We greatly mourn his passing."