"It is the first major blow against FARC since President Santos ordered the resumption of air strikes against the guerrillas on April 15," the Defence Ministry official said, speaking on condition of anonymity.
The attack involved both military and police and took place took place in Guapi in the Cauca region of western Colombia, a FARC stronghold and an area popular with drug cartels.
The army targeted a unit of the Revolutionary Armed Forces of Colombia (FARC) that it blames for an attack in November on Gorgona island that killed one of its lieutenants, the source said.
Santos lifted the air strike suspension against the group after the Marxist guerrillas were suspected in the killing of 10 soldiers in an attack last month.