Iraq may be on the brink of its biggest crisis since 2006, when a civil war threatened to topple its nascent democratic system. Government formation talks have dragged out as pro- and anti-Iranian factions jockey for influence. Corruption and basic governance failures have triggered mass protests—particularly in Basra, Iraq’s second-largest city and primary oil-export hub. Armed militia factions are mobilizing. Iranian proxies have fired the first shots at the U.S. Embassy since 2014, showing their intent to use force to accomplish political goals. All this raises the prospect of an intra-Shiite civil war.

Such...