BAGHDAD—Iraqi authorities deployed troops across the country’s south and blocked access to the internet as protests over poor government services grew violent, with demonstrators breaking into oil facilities, burning political-party offices and shutting Najaf Airport.

The protests were fueled by dissatisfaction with corruption and services, which helped populist cleric Moqtada al-Sadr record an upset victory in May’s national elections. Demonstrators have complained about dirty drinking water, pollution, unemployment and a...