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The AIKS was one of the petitioners that had challenged the notification issued by the Environment Ministry on May 25.
Calling the development a "peasants' victory", it said the apex court "will empower secular forces".
It said the government appeared to be under "severe pressure" due to the ongoing peasants' struggle demanding withdrawal of the notification banning cattle trade.
"Thus the victory of the joint struggle by the peasants," the release said.
In its petition, AIKS had said the notification would "choke free movement of animals via the market space" and "completely undermine the freedom and rights of farmers, traders and all others whose livelihoods are linked to this production cycle".