WASHINGTON—Central Intelligence Agency Director Gina Haspel will brief Senate leaders Tuesday morning on what the spy agency knows about Saudi journalist Jamal Khashoggi’s death at the hands of Saudi operatives, people familiar with the matter said.

Ms. Haspel’s planned briefing follows criticism that the Trump administration received from several lawmakers last week after she failed to join an earlier briefing on Saudi policy conducted by Secretary of State Mike Pompeo and Defense Secretary Jim Mattis.

According...