WASHINGTON—A man shot by the FBI outside CIA headquarters when he got out of his car with a weapon has died, the FBI said on Tuesday. The man, who has not been identified, was shot at around 6 p.m. on Monday outside the heavily protected main gate of the CIA compound in suburban Langley, Virginia. The shooting followed a standoff that lasted for hours, an official familiar with the incident said. He was taken to a hospital, where he died of his wounds, the FBI’s Washington Field Office said in a statement. The FBI did not release additional details of what it called “an agent-involved shooting.” It said the shooting was under review and would not provide additional details.