Martínez is expected to be replaced with Rigoberto Urán for the individual time trial in Tokyo.
The 25-year-old was part of Ineos Grenadiers' successful Giro d'Italia squad, with Egan Bernal taking the overall win and Martínez finishing fifth.
However, just after the Giro, Martínez was infected with the coronavirus and has not managed to clear the virus.
Colombia will be represented by Esteban Chaves, Sergio Higuita, Nairo Quintana and Rigoberto Urán in the Olympic road race.
The Olympic Games road race takes place on July 24 and the time trial on July 28.
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