Humberside police were granted the extension last night (Sat Feb 9) and now have until 9.11pm tonight (Sun Feb 10) to question the 24-year-old man.
He was arrested on Wednesday (Feb 6) on suspicion of abducting 21-year-old Miss Squire, who was reported missing on February 1.
Detective Superintendent Mathew Hutchinson of Humberside Police, said: “I can confirm that the court has granted us a further 24 hours to question the man.
“We are still treating Libby’s disappearance as a missing person’s enquiry. I have said previously that we are keeping an open mind as to her whereabouts and that is still very much the case.
“Our number one priority is to find Libby Squire and we are still conducting extensive searches and appealing for any information from the public.”
Hull University philosophy student Miss Squire was reported missing from the city in the early hours of February 1 and an intensive search has been mounted by police and volunteers over the last week.
The address where the man was arrested is about half a mile from Miss Squire’s home.
Officers have said Miss Squire was dropped off in a taxi near her home on Wellesley Avenue at 11.29pm on Thursday January 31 and was seen 10 minutes later on CCTV near a bench on Beverley Road, where a motorist stopped to offer help.