SHANGHAI—A U.S. citizen related to the most senior Chinese politician jailed in President Xi Jinping’s anticorruption campaign said authorities in Beijing won’t let her leave the country, in a rare public airing of grievances by someone under an exit ban.

Huang Wan is known as Fiona and is married to the son of imprisoned former Chinese security chief Zhou Yongkang. In recent days, she has published documents and testimonials on Twitter that she said, in an interview, show how Chinese authorities have used legal maneuvers...