“The Supreme Court has characterized academic freedom as a special concern of the First Amendment,” said Ramya Krishnan, a lawyer at the Knight First Amendment Institute. “With so many Americans on TikTok, it’s important that researchers are able to study the impact that this platform is having on public discourse and society more generally.”

Representatives for Mr. Abbott, who announced the ban in December, did not immediately respond to a request for comment.

The lawsuit said that Jacqueline Vickery, an associate professor at the University of North Texas and a digital media scholar, had been forced to “suspend research projects and change her research agenda, alter her teaching methodology, and eliminate course material,” because of the ban.

Ms. Vickery was previously able to collect and analyze large numbers of TikTok videos for her work, which focuses on how young people use digital and social media for informal learning and activism, but she can no longer do this on her university-owned computers or internet networks, according to the suit. The Texas ban also appears to extend to her personal cellphone based on her use of university email and other apps there, the lawsuit said.

Ms. Vickery said in an interview that she had not been able to access TikTok since the university returned from winter break, even for an assignment where she wanted her students to read the privacy terms on TikTok’s site. The ban’s effect on her classes and research has been “really challenging,” particularly as she does not have a personal laptop, she said.