Parbatya Chattagram Jana Sanghati Samiti (PCJSS-Santu Larma) and United People’s Democratic Front (UPDF) have blamed each other for the incident.
The encounter took place in Jurgachharhi around 8.30am on Saturday, said Lakshmichharhi Police Station OC Bahar Miah.
Joy Kumar Chakma, who was killed in the crossfire, is a local businessman while injured Kolpo Rani Chakma is an eighth grader of Lakshmichharhi High School.
She was admitted to the district Sadar Hospital.
Jurgachharhi is a stronghold of JSS.
PCJSS Upazila unit president Jyotish Chakma said UPDF activists had attacked them.
However, UPDF media wing chief Niron Chakma denied the allegation.
Captain Imran Hossain of Guimara army camp said both the parties had exchanged several rounds of fire in the morning.
The army detained PCJSS activist Mangal Chakma and recovered a pipe gun, a pistol and four bullets from the spot.