The former Inter Milan and AS Roma player was arrested last week for being behind the wheel when his driver's licence had expired and was seen smoking an e-cigarette on the bench ahead of Sunday's 3-0 loss at Standard Liege, Belgian media reported.
"Clear agreements have also been made about what our club does and does not expect from the player," Antwerp said.
Antwerp, second in the First Division a point behind KRC Genk, added that ex-Belgium international Nainggolan and the club would not comment further as the team focuses on preparing for games against KV Oostende and Genk.
However, Nainggolan said on his Instagram account that he was very sorry for what he had done.
"The club has made a decision I can only accept, even though I think it might be a bit too severe for me. But I will try to contribute in one way or another," he added.