Three of the top cybersecurity officials at the Federal Bureau of Investigation are retiring from government service, according to people familiar with the matter—departures that come as cyberattacks are a major concern for the country’s security agencies.

Senior U.S. intelligence officials warn that the country is at a “critical point” facing unprecedented cyberthreats, including Russia’s ongoing attacks on the American political system. The retirements also come as the FBI is facing regular criticism from President Donald...