The 30-year-old sustained the injury in the first half of the team's 1-0 loss to Bolivia in El Alto last Thursday.
In a statement, the FCF said Martinez would travel to Argentina's capital Buenos Aires, to receive treatment with his club Racing.
In the 20th minute, Bolivia's Cuellar made a tackle from behind, and although it initially seemed like the impact wasn't severe but replays clearly showed Martínez's left ankle twisting awkwardly. Later, Medical tests, carried out in Barranquilla after the match, confirmed that the 30-year-old striker from Cartagena suffered a grade two sprained left ankle.
"The injury to his ankle prevents him from being 100% fit to face this commitment. The coach, his technical team and the group of players wish Roger Martínez a speedy recovery and return to activity," the FCF said.
Colombia and Chile will meet at Estadio Metropolitano in Barranquilla on Tuesday.
The Cafeteros are currently second in the South American zone standings with 16 points from nine qualifiers, three points behind leaders Argentina. Chile is last in the 10-team group with just five points so far.