Colombia were due to co-host the tournament alongside Argentina but tension in the country as a result of protests against the government have called for a change of venue.
Colombians have risen against the ruling government in recent months as a result of the introduction of controversial taxes, poor wages and a lack of opportunities for young people in the county.
Despite the disturbances in the country, Colombia were committed to hosting the tournament and even dialogued with CONMEBOL to reschedule the tournament to November but that proposition has been rejected.
The 2021 Copa America is due to run from June 13 to July 10 and will feature the 10 teams from South America.
"With regards to the Colombian government's formal request to reschedule the Copa America for November, CONMEBOL can reveal the following," the governing body said in a statement published on its official website.
"Due to reasons related to the international competition calendar and tournament logistics, it will be impossible to move the 2021 Copa America to November.
"CONMEBOL is grateful for the enthusiasm and commitment shown by the President of the Republic of Colombia, Ivan Duque and his collaborators, as well as by the president of the Colombian Football Federation, Ramon Jesurun, and his team. We are sure that in the future new projects together will emerge for the growth of Colombian and South American football.
"CONMEBOL can ensure the playing of the 2021 CONMEBOL Copa America and will reveal in the coming days the relocation of the games that were due to be played in Colombia."
