Falcao was returning to his club Atletico Madrid to recover, missing Friday's match with Venezuela and the clash with Argentina on Tuesday, both at the Metropolitano in the Caribbean port city of Barranquilla.
"During a normal movement in practice [on Wednesday], Falcao kicked the ball with his left leg and felt a pain in the adductor [muscle] of his right leg," doctor Carlos Ulloa told reporters.
"With the Venezuela match so close, less than 48 hours away, we think it prudent not to have him in mind for this match given the pain he is feeling."
Falcao scored Colombia's stoppage-time winning goal when they beat Bolivia in La Paz last month in their only qualifier so far in the South American group. There were two rounds of matches in October but Colombia had a bye in the first.
Coach Leonel Alvarez is expected to pick Mexico-based striker Jackson Martinez of Chiapas to take Falcao's place up front.
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