Saudi authorities arrested 11 princes for criticizing the government, the latest indication that the country’s rulers are moving to stamp out traces of internal dissent as they push through a painful economic transition.

Saudi Arabia’s attorney general said the princes were arrested after staging a sit-in outside a royal palace in Riyadh to protest the government’s decision to stop paying electricity and water bills for members of the extended royal family. He said they were also asking for compensation for the execution of...