The warning was issued after the G8 leaders expressed "serious concern" over the last month's post-election unrest which left at least 20 people dead.
Groups of students have held small commemorative gatherings in previous years, but Morteza Tamadon, the governor of Tehran, issued a blunt warning for this year's anniversary.
"If some people make moves that are contrary to security initiatives under the influence of anti-revolutionary networks, they will be trampled under the feet of our alert people," he told the official IRNA news agency.
Witnesses said leaflets had been handed out in several Tehran squares urging people to join Thursday's gathering.
The Iranian authorities have banned all gatherings amid a crackdown on protesters, reformists, journalists and political activists who have opposed the re-election of Mahmoud Ahmadinejad.