Prohibitory orders under Sec 144 have been clamped on the town after the clashes.
The local administration said the prohibitory orders enforced on Saturday will stay in effect until further notice.
The clash erupted around 10am at the Court Building area in the city, said Kotwali police OC Sohel Imtiaz.
OC Imtiaz himself was hurt during the clash and later given first aid.
The nine other victims were admitted to the Rangamati Sadar Hospital.
They were identified as 'Ibrahim', 24, Alamgir, 27, 'Jahirul', 27, 'Monir', 21, 'Harun', 27, Jabbar Hossain, 50, Jamal Hossain, 25, Zakir Hossain, 32, and Md Manik, 21.
The government has opened six medical colleges in Tangail, Jamalpur, Patuakhali, Sirajganj, Manikganj and Rangamati and five in others places. All of them are under the tutelage of Bangladesh Army.
Pahari Chhatra Parishad (PCP) called for an all-day-long blockade in protest in Rangamati against the government decision.
When the PCP supporters took to the streets with other supporting the blockade, the ruling party supporters tried to stop them.
That sparked the clash.
The PCP has said the medical college should not be started until the 1997 peace treaty was implemented.
Dhaka University’s sociology teacher Sadeka Halim was in Rangamati during the conflict.
She said the situation was tense on Friday as locals feared a clash on Saturday in the town.
People who celebrated the inauguration of a medical college there fought pitched battles blockade campaigners.
The former information commissioner said the implementation of the 1997 CHT Peace Accord was crucial to ensure tranquillity in the turbulent region.
She said the locals needed a well-equipped hospital more than a medical college now.