A patrol conducted the drive on Burighat near Naniarchar on Tuesday afternoon to catch 'extortionists' from the UPDF faction led by Prasit Bikash Khisa, the Inter Service Public Relations Directorate or ISPR said in a statement.
The gunfight erupted when the suspects opened fire on the Army patrol, it claimed.
A soldier, Shahabuddin, received bullet injury in his left shoulder. He was airlifted to the Combined Military Hospital in Chattogram for treatment.
The Army recovered an AK-22 SMG from the site.
A 20-strong team of the Army took part in the operation, said Alamgir Kabir, superintendent of police in Rangamati.
Aungyo Marma, a spokesman for UPDF, told reporters that they were unaware of any such incident.