According to a judicial decision in the case, a federal appeals court will allow Texas' new social media legislation to take effect after a lower court struck down a preliminary injunction.
The Texas law, known as HB 20, empowers anyone to sue technology companies for alleged censorship.
The ruling is a setback for tech companies that had argued that the regulation was illegal under the First Amendment.
The parties that had challenged the law in court, CCIA and NetChoice, did not immediately reply to a request for comment.
The US Court of Appeals for the Fifth Circuit's judgment raises the question of whether it might be appealed to the Supreme Court.