Rodrigues has suffered a number of injury problems in his debut season in England, restricting him to 26 appearances across all competitions.
The 29-year-old played just one of Everton’s final six league games due to a calf problem and was released early by the Toffees to recuperate in time for national team duty.
However, after tests were conducted on the former FC Porto and AS Monaco man, Colombia have deemed him not fit enough to contribute in their upcoming matches.
A statement from the Colombian FA read: "The coaching staff of the Colombia men's senior team reports that the player James Rodriguez has been ruled out for the games against Peru and Argentina for the qualifiers for the FIFA World Cup Qatar 2022, and the CONMEBOL Copa America 2021.
"In recent days, the midfielder was subjected to medical examinations, which determined that he is not at the optimal level of competition, therefore he will not be able to join the group called by Reinaldo Rueda for the aforementioned commitments and the South American championship.
"The coach and his team of collaborators regret not being able to count on James this time and hope that soon the midfielder will be able to be part of a squad, representing our country with the height and professionalism as he has always done."
Rodriguez has expressed disappointment with the decision taken by the Colombia coaching staff with a statement on social media that reads: “Enough time has been taken to integrate (me) into the full range of conditions for football practice and this way it will not affect my participation in the next fixtures of our national team.
“With surprise I receive the statement from the main technical body stating that they do not count on me and wishing me a full recovery.
“(This) has me deeply disappointed. Failing to receive the confidence of the technical team breaks with everything and generates an enormous pain.”