The military also seized six rifles, two pistols, explosives, grenades and weapons suppliers after the fighting on Saturday in Narino province, near the border with Ecuador, General Leonardo Barrero said.
The FARC -- the Revolutionary Armed Forces of Colombia -- is the country's largest leftist guerrilla group, and the insurgency it has waged since 1964 is the oldest in Latin America.
Since November, the guerrillas have been engaged in peace talks with the government, though clashes have continued in the absence of a ceasefire agreement.
In Narino, the FARC along with Colombia's second-largest guerrilla group the ELN and criminal gangs of ex-paramilitaries and drug cartels, have battled over the past 20 years to control the illegal cultivation and export of cocaine and marijuana through Colombia's Pacific coast.