The Monaco striker had been in major doubt for the tournament since damaging his cruciate knee ligament in a Coupe de France tie against Monts d'Or Azergues in January.
Colombia coach Jose Pekerman included the forward in his provisional 29-man party announced on May 13, in the hope the 28-year-old recovered in time for their opening Group C encounter with Greece on June 14.
However, it emerged on Monday that Falcao had not recovered sufficiently to be included in the squad, in a huge blow to the nation's prospects.
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