The program aired on the Saudi-owned MBC TV showed a man dressed like the black turbaned Hassan Nasrallah taking orders from Iranians.
The program comes amid rising tension between the Iran-backed Hezbollah and Saudi Arabia over the wars in Yemen and Syria.
Lebanon's state-run National News Agency reported that Hezbollah supporters closed roads with burning tires in different areas including the suburbs of Beirut and the eastern Bekaa Valley.
The protests began Saturday night and several roads were closed on Sunday.
The Lebanese army said in a statement that troops were deployed in several areas around Lebanon to prevent any violence.
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