W ASHINGTON—Health and Human Services Secretary Robert F. Kennedy Jr. top aides have become embroiled in personality clashes, culminating this week in a White House-backed shake-up to calm infighting at the department.

Kennedy Jr. has fired two of his top aides in an abrupt shakeup of the leadership at the nation’s sprawling health department, two people familiar with the matter told CNN. Kennedy this week ousted chief of staff Heather Flick Melanson and deputy chief of staff for policy Hannah Anderson,

U.S. Health and Human Services Secretary Robert F. Kennedy Jr. has fired two top leaders at the department, chief of staff Heather Flick Melanson and deputy chief of staff for policy Hannah Anderson,