Shiite cleric Moqtada al-Sadr traveled to Iran on Monday, a top aide said, a day after hundreds of his supporters withdrew from Iraq’s fortified International Zone following protests that paralyzed the government. Ibrahim Al Jaberi, head of the Sadr office in Baghdad, said the cleric had departed for Iran Monday, but provided no other details on his itinerary. The cleric’s travel to Iran could provide some indication of whether Mr. Sadr might turn to Tehran to help resolve the current standoff with the Iraqi government and smooth over divisions within his own Shiite community. The protests have surfaced simmering tensions. Some of Mr. Sadr’s supporters are angry not only with government mismanagement but also with Iran’s influence in Iraq. Tehran has funded and equipped Shiite militias to help combat Islamic State, which now controls Iraq’s second largest city, Mosul. Yet the Iran-backed militias have become powerful in their own right, on par now with the country’s army.Many of Mr. Sadr’s supporters could be heard chanting anti-Iranian slogans during the weekend protests—chants that are likely to offend mainstream Iraqi Shiites who consider Iran critical to the fight against Islamic State.