The world needed to know Muslims "would not be silent in the face of this insult", Sheikh Hassan Nasrallah said.
Protests at many US diplomatic missions have been continuing over the film, which was made in the US.
One person was reportedly killed in clashes between protesters and police in Pakistan on Sunday.
In a speech broadcast on Hezbollah's Al-Manar TV station, Sheikh Nasrallah called for demonstrations on several days over the coming week.
The first is scheduled to take place on Monday afternoon in a southern suburb of Beirut which is a Hezbollah stronghold.
Sheikh Nasrallah branded the video the most dangerous insult to Islam ever, worse, he said, than Salman Rushdie's novel The Satanic Verses and the cartoons of the Prophet Muhammad, which were published in a Danish newspaper in 2005.
He said he had waited for the Pope to complete his three-day official visit to Lebanon before speaking out on the matter.
"Those who should be held accountable, punished, prosecuted and boycotted are those directly responsible for this film and those who stand behind them and those who support and protect them, primarily the United States of America," Sheikh Nasrallah said.
He said that Arab and Islamic governments should press for an enforceable international law banning insults to Islam and other religions.
There have been protests over the film in Lebanon in recent days, but most have been reported from the northern city of Tripoli, which has a Sunni Muslim majority.
The obscure, poorly-made film at the centre of the row, entitled Innocence of Muslims, depicts the Prophet Muhammad as a power-hungry and foolish man, and includes scenes of him having sex with his wife Khadija and other women.