WASHINGTON—Most of Hillary Clinton’s emails recovered during a Federal Bureau of Investigation probe into practices from her time as secretary of state won’t be made public until after Election Day, according to a new timetable set Friday by a federal judge.

Judge James Boasberg on Friday ordered the State Department to finish processing 1,050 pages of material for release by Nov. 4—just a fraction of what could be as much as 10,000 pages of material.

The...