Eto'o was cleared of indiscipline by Fecafoot while Tottenham's Benoit Assou-Ekotto was reprimanded.
The charges all related to the Africa Cup of Nations qualifier against Senegal on 4 June and the training camp before the match.
Song had refused shake hands with Eto'o when the pair met before the game.
They had fallen out during the 2010 World Cup in South Africa and the match against Senegal marked Song's return to the squad.
Song has been fined approximately US$2,000, severely reprimanded and ordered to carry out three days' training with young players within the next year.
Eto'o was accused of missing a training session and showing indiscipline to coach Javier Clemente when the player disputed a substitution during the game.
He has been cleared of the charges.
Assou-Ekotto, who did not attend the hearing, has been given a warning after failing to respond to a call-up from Clemente.
The Indomitable Lions are struggling in their campaign to reach the Africa Cup of Nations in Equatorial Guinea and Gabon next year.
They currently lie third in their group, with five points from four games so far.
They are five points behind leaders Senegal and two behind DR Congo.
Source.