Samaikyandhra Students Joint Action Committee organised the protest near Public Garden.
Students from 14 universities from Andhra and Rayalaseema took part in the demonstration, the organisers said.
Over two dozen members of the committee were taken into custody during the protest, police said.
The student leaders said they submitted a memorandum to Hyderabad Police Commissioner Anurag Sharma seeking permission for a public meeting on January 21.
Police prevented the committee members from continuing the protest and took them into preventive custody even as they raised slogans. At least 25 protesters were taken into custody and later released, a senior police officer said.
Asked about nod for the meeting, the officer said the matter was under consideration.