The clashes came as a group of Iranian students issued a call for mass protests against Ahmadinejad to coincide with the annual event.
"Police fired tear gas at groups of protesters chanting slogans against President Mahmoud Ahmadinejad in Vali Asr intersection and Enghelab Street," a witness told AFP, referring to prominent locations in central Tehran.
The protesters were chanting "Death to the Dictator" and "Do not be scared. We are all together," the witness said, adding that some protesters also beat up a policeman.
AFP could not independently confirm the incidents as foreign media have been banned from covering Monday's event.
Students of Tehran's prestigious Amir Kabir University had earlier urged protests against Ahmadinejad, in an online statement.
"We are asking all people to come to universities so we can have one voice to protest at the coup d'etat," said the statement, issued by the group going under the name "Green university students of Iranian universities."
Green was the signature colour of main opposition leader Mir Hossein Mousavi's election campaign for the June 12 presidential poll. He lost to Ahmadinejad in what he claims was a "fraudulent" election staged to return the hardliner to power.
Since then his supporters have taken to streets in Tehran at the slightest opportunity to demonstrate against Ahmadinejad, accusing him of "stealing their votes."
Hundreds of thousands of protesters poured onto streets in the immediate aftermath of the poll and in the deadly unrest that followed dozens were killed and thousands arrested.
The defiant protests shook the pillars of the Iranian regime in what was one of its worst crises since the 1979 Islamic revolution.
Around 140 top reformists, political activists, and journalists have also been brought to court in what opposition leaders claim to be "show trials."
The elite Revolutionary Guards have warned they will crack down on any attempt by regime opponents to hijack the annual Students Day, which marks the 1953 killing by the shah's security forces of three students, just months after a US-backed coup toppled popular prime minister Mohammad Mossadeq.
At Tehran's Sharif University, meanwhile, a group of students marked Students Day by staging a symbolic funeral procession in honour of the three students slain in the 1953 incident.
They shouted slogans such as "Allahu Akbar", "Death to America" and "Students will die but will not accept humiliation," Fars news agency reported.
Anticipating mass protests, hundreds of police have been deployed around Tehran University, one of the city's most politically sensitive institutions, to prevent the protests, witnesses told AFP.
"Police have also cordoned off side lanes going towards Tehran university," a witness said.
Neither Mousavi nor another opposition leader Mehdi Karroubi have issued direct calls for protests on Monday, but the former has challenged the authorities as they moved to prevent them.
"If you silence all the universities, what can you do with the situation of the society?" Mousavi asked in a statement posted on his website Kaleme.com.
He warned Iranian authorities they are "fighting with shadows in the streets," referring to protesters.
The conservative bloc of Iran's parliament, meanwhile, urged opposition figures to give up their "political obstinacy."
"… we have ample proof the reformists wanted to substitute the Islamic regime with a secular democracy" after the election, the official IRNA news agency quoted the statement as saying.
"… we recommend to the gentlemen to give up their behaviour which smells of political obstinacy."
The hardline Kayhan newspaper warned students to be cautious as the "hypocritic network (anti-revolutionary groups) want to cause casualties among the students participating in opposition gatherings and blame it on the regime."
Aside from banning the foreign media from covering Monday's events, the authorities have also cut Internet connections and blocked access to several opposition websites.
