Known by its French initials FILA, the organization says it is "greatly astonished" by the IOC executive board decision.
FILA says it will take "all necessary measures" to convince IOC members to maintain wrestling's Olympic status when they meet in Buenos Aires, Argentina, in September.
Still, FILA President Raphael Martinetti faces criticism when his ruling board meets this weekend in Thailand.
Russian federation leader Mikhail Mamiashvili says FILA is the problem, and Martinetti's tasks include defending "wrestling's place before the IOC."
German official Jannis Zamanduridis says "a piece of the Olympic idea is dying with this decision."