Young men had originally gathered around 9:30 pm in the southern Beirut suburb of Msharrafieh to protest the two-and-a-half-minute skit on MBC's "WiFi" comedy program showing a man impersonating Nasrallah.
There, they shouted slogans calling for the death of the Saudi royal family and expressing their loyalty to Nasrallah.
The protests quickly spread to other areas around Beirut where some protesters blocked roads with burning tires, the Daily Star reported.
The army said in a statement that it had deployed to several areas around the capital and set up checkpoints to contain the protests.
Protesters also blocked a road at the entrance of Baalbek in northeast Lebanon.
No violence or damage to property was reported, and all roads around the capital were reopened.
The incident comes as tensions soar between Hezbollah and Saudi Arabia over long-simmering disputes.