The 25-year-old man was arrested by Humberside Police on Wednesday, but has today been released as detectives continue to investigate the student's murder.
Detective Superintendent Martin Smalley said: “Proceedings are active and I would remind people to please refrain from any speculation, as the investigation is very much live and continuing.
“There are further enquiries still being carried out and there are constant investigative developments and procedures that are ongoing.
“The majority of the additional analysis stage is now complete, with a small number still pending final results.
“My heartfelt thanks go out to Libby’s parents for their continued understanding and patience.
"They have been kept informed of all the developments in the investigation and they will always maintain our support.”
University of Hull student Libby was last seen just after midnight on Friday, February 1 on Beverley Road, close to the junction with Haworth Street.
An extensive search of the areas around her home on Wellesley Avenue was carried out and police confirmed the body of a woman found near Spurn Point was hers.
Police have been investigating Libby's death as a homicide.