SHANGHAI—China’s high-reaching anticorruption campaign is heading toward its next phase—prosecution—carrying risks for the leadership to prove allegations that have mounted without much evidence for two years.

Prosecutors announced the criminal indictment Friday of Zhou Yongkang, formerly one of the nine most senior officials in the ruling Communist Party. Chinese President Xi Jinping has pursued an anticorruption campaign that has remade politics and that at times seemed to disproportionately focus on Mr. Zhou and people...