WASHINGTON—A news report that Central Intelligence Agency Director John Brennan’s private email account was hacked by a high-school student has prompted the agency to refer the matter to “appropriate authorities,” a spokesman said Monday.

The New York Post reported on Sunday that a “teen stoner” claims to have hacked into Mr. Brennan’s AOL account and accessed sensitive files, including his application for top-secret security clearance. The newspaper also alleged Social Security numbers and other personal information for numerous...