The violence happened early Saturday after forest rangers confronted a gang of more than 50 men illegally felling trees in the Chittagong region, the private UNB agency said.
"As the forest guards challenged them, the thieves opened fire," a source told the agency.
Motaleb Hossain, 45, died instantly and 10 colleagues were injured in the shooting. Among the wounded, four remained in hospital Saturday in a critical condition, the agency added.
Enviornmentalists say timber thieves strip Bangladeshi forests of millions of dollars worth of trees each year, sometimes in connivance with forestry officials.
An estimated 70,000 hectares (172,900 acres) is lost annually to illegal logging and other causes of deforestation such as urbanisation and the demand for agricultural land.
Experts predict that if the rate of deforestation continues Bangladesh will have lost all forest cover within 40 years, threatening a range of bird, animal and plant species.
Police have launched an investigation into the shooting.