The attack on Tuesday is the worst blow against the military in at least three years, the army said.
An army spokesman said the Revolutionary Armed Forces of Colombia (FARC) attacked the soldiers near the town of Vista Hermosa in Meta province.
Details of the attack were not immediately available but the military toll was the worst for any single incident since Alvaro Uribe, the country's president, took office in late 2002 promising to crack down on the rebel army.
The soldiers were providing security for another army team which was manually destroying coca plants, the army said. Coca leaf is the raw material of cocaine.
The 17,000-strong FARC, which has been fighting for socialist revolution since 1964, draws much of its money from the cocaine trade.
The peasant militia, which has little support in Colombia's cities, has staged several big attacks this year after a period of relative inactivity when Uribe stepped up military action against them.
Violence has fallen sharply during the Uribe government and polls say the right-wing president should easily win re-election next May.
But thousands of people are still killed in fighting in Colombia every year and at least 400 military personnel have been killed so far this year.