Clashes between Jatiyatabadi Chhatra Dal and Islami Chhatra Shibir were reported at Government Tolaram College in Narayanganj and Barishal University during programmes marking July Mass Uprising Day.
Police and university or college authorities intervened to bring the situations under control.
In Narayanganj, the confrontation began after an exchange of words over remarks at a college event, police said.
Witnesses described repeated confrontations involving brick throwing, sticks and rods near the college campus and in the surrounding area.
Narayanganj Chhatra Dal leader Monir Hossain Zia alleged that Shibir activists made disorderly remarks and assaulted Chhatra Dal members.
Narayanganj metropolitan Shibir president Amit Hasan alleged that Chhatra Dal activists assaulted three Tolaram College Shibir office-bearers, prompting others to go to the area.
College principal Md Shahidul Islam said he was informed that an injury had occurred outside the gate after the programme and that the administration alerted authorities.
The number injured in Narayanganj remains unclear: one account put the total at 20, while another put it at 10.
Narayanganj police said they would review CCTV footage and take legal action against those found responsible.
At Barishal University, two rounds of clashes were reported, with at least 20 people said to have been injured.
Ten injured people were reported admitted to Sher-e-Bangla Medical College Hospital.
Chhatra Dal alleged that Shibir entered the campus with outsiders and attacked its members after being challenged.
Shibir alleged that Chhatra Dal attacked its procession commemorating those killed in the 2024 uprising.
Barishal University proctor Mehedi Hasan Sohag said the clash stemmed from a misunderstanding and that teachers and administrative personnel were injured while trying to stop it.
A senior metropolitan police officer said police and university authorities restored calm at the Barishal campus.