The suspect, described as a bearded and balding man, knocked on the door of the home of Ruthanne Lodato, 59, Thursday and shot her and her caregiver when they answered the door, the Washington Post reported Friday.
The unidentified caregiver, a woman, is expected to survive, police said.
"We are concerned, and the citizens should be concerned," Alexandria Police Chief Earl Cook said, noting similarities between the incident and the death three months ago of prominent regional transportation planner Ronald Kirby, 69, who was shot to death in his home less than a mile from Lodato's home.
Thursday's shooting prompted an extensive manhunt involving police with dogs, a police helicopter and the lockdown of several schools in the area, the newspaper said.
An unidentified neighbor said Lodato is part of a prominent local family, with a brother and her late father both former Alexandria-area judges.