Five other FARC members were captured, Colombia Reports said Tuesday.
A statement by the military's commanding general said intelligence gathered by the national police allowed the military to locate a "concentration of terrorists" who had orders from FARC leadership "to carry out terrorist actions of national impact."
The statement said in the previous 24 hours the military had "neutralized 31 terrorists, of them, 21 killed in combat, and 10 captured."
Colombian President Juan Manuel Santos, the country's former defense minister, confirmed the battle and urged the army to "continue the offensive as if there were not dialogue in Havana."
FARC and the government have been engaged in peace talks in Cuba since November 2012.
FARC is the Spanish acronym for Revolutionary Armed Forces of Colombia.