Cavani is serving a three-match ban after using the word 'negrito' on Instagram while thanking a friend for complimenting him on his match-winning performance in a 3-2 victory at Southampton last month.
The Uruguay international deleted the post, apologised and chose not to contest the misconduct charge out of respect for the FA's fight against racism within football but insisted there was no malicious intent.
On Monday, the Uruguayans player's union called on the FA to overturn Cavani's ban, describing their decision as "a true discriminatory act" and "against Uruguayan culture" and Conmebol has now followed suit.
In a statement published on Tuesday, the confederation said: "Conmebol expresses its solidarity with the player Edinson Cavani, sanctioned by the Football Federation of England.
"The disciplinary measure for the outstanding player of the Uruguayan team clearly does not consider the cultural characteristics and the use of certain terms in Uruguay's everyday speech.
"The judgment of these types of statements, within the framework of a process that can lead to penalties for the athlete and that affect his reputation and good name, must always be carried out taking into account the context in which they were made and, above all, cultural peculiarities of each player and each country.
"Conmebol condemns and will always condemn with the greatest energy any racist or discriminatory manifestation, but the specific case for which Cavani was sanctioned does not constitute one of them."
Cavani was also fined £100,000 and must complete an education course as part of his punishment.
The 33-year-old has already served one instalment of his three-match ban and will now miss Wednesday's EFL Cup semi-final against Manchester City and Saturday's FA Cup third round tie against Watford.