Jackson posted the message after Ibaka and Los Angeles Lakers forward Metta World Peace got tied up during the fourth quarter of the Thunder's 114-108 victory on Friday night.
The post has since been deleted, but multiple outlets reported it read: "Somebody tell serg Abaka. He aint bout dis life. Next time he run up on me im goin in his mouth. That's a promise. He doin 2 much."
"The recent public comments made by Stephen Jackson are absolutely unacceptable, cannot be tolerated and do not reflect the standards held by the San Antonio Spurs," Spurs general manager RC Buford said Sunday night in an emailed statement.
The team said Jackson would be fined, but the punishment would "be imposed in consultation and co-ordination between the Spurs and the NBA."
It was unclear if Jackson faced additional punishment from San Antonio in the wake of the NBA fine.
Jackson apologized to Ibaka on Twitter on Sunday, calling his post "unprofessional and childish."
Jackson has played for seven different teams in 13 seasons in the NBA. He is perhaps best known for his role in the Pacers-Pistons brawl in 2004, which also involved World Peace -- then known as Ron Artest -- and resulted in a 30-game suspension for Jackson.