The 29-year-old suffered the injury in March and has been unable to train with Colombia's squad at their World Cup camp in Buenos Aires this week, reports Xinhua.
"Physically he is not right and there is not enough time for him to recuperate for the World Cup," Colombia's Argentine coach Jose Pekerman said here Wednesday.
"Players have to be at their peak. We are very sorry for Edwin, but unfortunately that's football."
Valencia joins America defender Aquivaldo Mosquera, Mainz midfielder Elkin Soto and Al Shabab midfielder Macnelly Torres as those to have been cut from Pekerman's provisional 30-man squad. Another three players will be trimmed by June 2.
Monaco striker Radamel Falcao, who is recovering from surgery to repair torn cruciate ligaments in his left knee in January, remains in a race against time to be fit for the June 12-July 13 tournament.
"We'll wait for Falcao until the last day, the last minute," Pekerman said. "We have a lot of people to make the final decision. We'll find the most logical reasons with the player and doctors."
Colombia have been draw in the World Cup's Group C alongside Greece, Cote D'Ivoire and Japan.