The political organization of Virginia Gov. Terry McAuliffe, an influential Democrat with longstanding ties to Bill and Hillary Clinton, gave nearly $500,000 to the election campaign of the wife of an official at the Federal Bureau of Investigation who later helped oversee the investigation into Mrs. Clinton’s email use.

Campaign finance records show Mr. McAuliffe’s political-action committee donated $467,500 to the 2015 state Senate campaign of Dr. Jill McCabe, who is married to Andrew McCabe, now the deputy director of the...