Iran's Ministry of Education said several students were treated by emergency services for a drop in blood pressure, but denied that security forces had entered the school.
Videos circulating on social media showed heavily armed security forces outside the school. One clip showed them on motorbikes and firing at least one teargas canister. Reuters could not independently verify the authenticity of the footage.
Unrest ignited by the death of Mahsa Amini, a 22-year-old Kurdish Iranian woman who was detained by the Islamic Republic's morality police for “improper attire” and died in police custody, has swept Iran for five weeks. Rights groups say more than 200 people have been killed in the crackdown.
Women have played a prominent part in the protests, removing and burning veils. The deaths of several teenaged girls reportedly killed during protests have fuelled more anger.
Demonstrations continued on Monday, with a rally at a university in the western city of Hamedan, and students shouting down a government spokesman who visited a Tehran university, according to students and rights groups.
The education ministry said there was a clash at the Tehran high school between staff, students and parents after the school principal insisted on checking the girls' phones.
The widely followed activist Twitter account Tasvir1500 said uniformed forces attacked the school and at least one girl was wounded, but the city police denied their account.
“After news of a conflict near a high school ... police were dispatched to the area and investigated the issue which turned out to be a fight between a number of thugs,” Tehran police said, adding that agitators were identified and arrested.
Rights groups say thousands of people have been arrested in the crackdown, which started in Amini's hometown of Saqez in northwest Iran before spreading across the country.
Protesters have called for an end to the religious clerical rule which has governed Iran since the 1979 Islamic Revolution, and for the overthrow of Supreme Leader Ayatollah Ali Khamenei.
A court in Tehran on Monday indicted some 315 people arrested in recent “riots” for “gathering and conspiring with intent to damage national security, propaganda against the system and igniting public disorder,” state news agency IRNA reported, citing a judiciary official.
Four of the detainees have been charged as mohareb (enemies of God). Under Iran's interpretation of Sharia law the sentence for a guilty verdict is execution.
Fars news agency said 10 people had been arrested in northwest Iran for working with Israel's intelligence agency Mossad. Iran and Israel are longtime foes. Israel accuses Iran of backing militant attacks against it, while Iran says Israel has carried out a number of killings of Iranian officials.
Videos on social media showed anti-government protests at several universities, with students chanting “Death to Khamenei”.
Khamenei has warned that nobody should dare think they can uproot the Islamic Republic, and has accused adversaries of fomenting the unrest. State TV has reported the deaths of at least 26 security force members.
At the Khajeh Nasir University in Tehran, video footage showed government spokesman Ali Bahadori Jahromi being interrupted with chants of “Woman, Life, Freedom” as he addressed students, who also shouted: “We don't want a corrupt system, we don't want a murderous guest”.