The strike followed a row over bonuses after a tournament in Morocco in November and led to the cancellation of a friendly against Algeria.
The Cameroon captain, 30, has 10 days to appeal against the ban.
Vice-captain Enoh Eyong received a two-match ban, while Tottenham's Benoit Assou-Ekotto was fined $1,980 (£1,276).
The decision was published on the federation's website on Friday.
The federation said Eto'o was banned for "violating the internal regulations of the national team relating to loyalty and obligation of participating in a match".
Cameroon have failed to qualify for the 2012 Africa Cup of Nations finals, so the first games Eto'o will miss are the Indomitable Lions' opening games in qualifying for the 2013 Africa Cup of Nations and the 2014 World Cup.
Cameroon begin their bid to reach the 2013 Nations Cup finals against Guinea Bissau on 29 February, with the return leg of the tie on 17 June.
They start their quest to reach the 2014 World Cup in Brazil with a match on 1 June against DR Congo.
Eto'o is the most decorated player in African history having won the European Champions League three times during his time at Barcelona and Inter Milan.
He has been named African Footballer of the Year four times and won an Olympic gold medal with Cameroon in 2000 and the Africa Cup of Nations in 2000 and 2002.
Eto'o moved to Russian club Anzhi Makhachkala in August 2011, becoming one of the best paid sportsmen in the world.
Editor's Note: this article was originally published on bbc.com