WASHINGTON—The State Department will pause its internal review of classified information found on former Secretary of State Hillary Clinton’s personal email server until the Federal Bureau of Investigation completes its own probe, a spokeswoman said Friday.

“We do not want our internal review to complicate or impede the progress of their ongoing law-enforcement investigation,” State Department spokeswoman Elizabeth Trudeau told reporters at a briefing Friday. “The internal review is on hold, pending completion of the FBI’s...