Fernandez, 30, suffered a meniscal injury in his left knee which will keep him out for several weeks, meaning he will miss the special-edition Copa held in the United States, starting Friday.
The Fiorentina midfielder was flown back to his homeland and will begin treatment with the locally-based medical staff of the Chilean national team.
"The decision was taken because the athlete had a twist in his left knee that caused a joint blockade during training on Monday," a statement on the Chilean Football Federation (AFP) website read on Wednesday.
"The player was unable to partake in any physical activity the next day, suggesting a medial meniscal injury, which disables him for training and sports competition."
A decision has yet to be made on who will replace Fernandez in Juan Antonio Pizzi's 23-man squad.
Defending Copa champions Chile begin their tournament on June 6 in a rematch of the 2015 final against Argentina, before facing fellow Group D opponents Bolivia (June 10) and Panama (June 14).