The guard is the country's most powerful military force and is tasked with defending the clerical regime that came to power in Iran in 1979 under Khomeini's leadership after the pro-U.S. shah was overthrown.
"The Guard ... won't tolerate any silence or hesitation in the immediate identification, trial and punishment of those carrying out this ugly insult and the agents behind them," the Guard said in a statement posted on its website.
Television cameras caught images of students tearing up Khomeini's photo during anti-government protests last week and the images have been repeatedly broadcast on state TV. Khomeini remains widely respected and revered in Iran.
The opposition maintains that those were isolated incidents and are being used by the regime to discredit the reformists, who are protesting what they say were rigged presidential elections in June.
The Dec. 7 rallies did see widespread attacks on Khomeini's successor, Ayatollah Ali Khamenei, the current supreme leader of the country.
Students chanted slogans against him, burned and trampled his photos in unprecedented acts of defiance in a country where Khamenei has final say in all state matters.
The actions of the students reflect how a protest movement that began by rejecting President Mahmoud Ahmadinejad's June 12 re-election has evolved to confront the country's ruling theocracy.