Alireza Ronaghi, Al Jazeera's correspondent in Tehran, said mobile phone communications in areas where protests were expected had been jammed.
He said police were stopping pedestrians from getting anywhere near campuses, and described the situation as "escalating".
Ahead of Student Day, several websites had called for demonstrations at universities.
Witnesses at Tehran University said hundreds of riot police and Revolutionary Guard members armed with tear gas, batons and firearms had surrounded the campus.
"There are hundreds of riot police, everywhere around Tehran University and nearby streets," a witness told the Reuters news agency.
Tehran residents said internet access, including to email and websites loyal to the political opposition had been limited.
Student Day marks the killing of three students at an anti-US protest in 1953 under the Shah, who ruled Iran before the Islamic revolution of 1979.
Since the 1990s, the occasion has also served as an opportunity for protests calling for increased social and political freedoms.
Hundreds of thousands of people demonstrated in June in the wake of the re-election of Mahmoud Ahmadinejad as president, claiming that the Iranian authorities had rigged the vote.
|Student Day marks the killing of three students at an anti-US protest in 1953 [AFP]
Dozens were killed in clashes with security forces and hundreds more were detained by the authorities.
The Student Day crackdown follows in the wake of the election protests.
Mir Hossein Mousavi, the main rival to Ahmadinejad in the elections, said on his website that the reform movement was still alive despite pressure from the clerical establishment.
"Let's say you suppressed students and silenced them. What will you do with the social realities?" his Kaleme website quoted him as saying, referring to the arrests of students in Tehran and other cities that have taken place in the past few days.
"You [the authorities] do not tolerate the student day rallies. What will you do on the following days?"
The official news agency IRNA on Monday offered a different view, saying that the opposition movement would fail to gather support on Student Day and described it as the "last nail of the coffin" of the protests which followed the disputed June 12 election.