WASHINGTON—The U.S. government has developed a specially designed, secret missile for pinpoint airstrikes that kill terrorist leaders with no explosion, drastically reducing damage and minimizing the chances of civilian casualties, multiple current and former U.S. officials said.

Both the Central Intelligence Agency and the Pentagon have used the weapon while closely guarding its existence. A modified version of the well-known Hellfire missile, the weapon carries an inert warhead. Instead of exploding, it is designed to plunge...