The acting chief of the federal Bureau of Prisons has been ousted from his post, Attorney General William Barr said on Monday, continuing the fallout over the suicide of disgraced financier Jeffrey Epstein in a New York detention facility that has struggled with staffing shortages and other problems.

Hugh Hurwitz, who had been serving as the head of the federal prison system on a temporary basis since May 2018, was reassigned to a different post, Mr. Barr said. The leadership changes come more than a week after Mr. Epstein,...