The appellate panel upheld a lower court's decision barring the couple from disparaging each other through social media.
The ruling, which has ignited a debate centering on First Amendment considerations, came following an ongoing war of words on Twitter since Nash's 2011 divorce from Alejandra Amarilla, The Daily Dot reported Wednesday.
The Arizona Court of Appeals said its ruling did not go against First Amendment free speech because Nash and his ex-wife had agreed to limit their speech under a joint custody agreement they filed at the time of their divorce.
The lower court ruling came in response to a "biting criticism" of the basketball star made on Twitter by Amarilla some time after the two split up. The court ruled neither Nash nor Amarilla would be allowed to conduct ongoing disparagement of each other through social media.
The court ruled Nash may have to pay additional child support beyond the "basic needs'" of their three children. The couple have joint custody of the children.