The nine came to the hospital on Saturday night, said Medical Police Outpost ASI Alauddin Talukdar.
They have been identified as Md Hamid Hossain, 40, Md Taher, 19, Abul Kalam, 35, Adija, 11, Fatema, 15, Bashir Ullah, 24, Manjur Rahman, 25, Karim Ullah 46, and Shamsul Alam, 35.
Shamsul Alam was injured in a road accident in Teknaf, but the others had been shot, ASI Talukdar said.
Eight of the wounded were initially taken to the Rohingya Refugee Camp Médecins Sans Frontières Hospital for treatment and then transferred to CMCH, he said.
A new wave of Rohingya refugees arrived in Bangladesh following attacks on police checkpoints and military camps in Rakhine state on Aug 25.
A total of 86 Rohingyas have been admitted to CMCH in the days since, mostly wounded by gunfire or explosions. Two of the patients have died.