Simunic, 35 playes for Dinamo Zagreb, led Croatia fans in a chant with pro-Nazi connotations following their 2-0 World Cup play-off win over Iceland.
“The salute was discriminatory and offended the dignity of a group of persons,” FIFA said in a statement.
Simunic, who denies political intent, was also fined 30,000 Swiss Francs. Following the win in Zagreb, Simunic, who has 105 caps for his country, shouted “for the homeland” over a microphone, to which fans respond “ready”.
The chant has associations with the Ustase, a fascist movement which was banned in 1945.
FIFA, said in a statement: “After taking into account all of the circumstances of the case, and particularly given the gravity of the incident, the committee decided to suspend the player for ten official matches.
“Moreover, the committee decided that the player will be banned from entering the confines of the stadiums with regard to the ten matches for which he is suspended.”
The first match of the ban will be the opening game of the 2014 tournament, when Croatia take on Brazil in Sao Paulo, with the remainder being served throughout the tournament and in future matches.
Australian-born Simunic is Croatia’s third-most capped player and has played in two World Cups and three European Championships.