Libby, 21, whose full name is Liberty Anna, went missing in the early hours last Friday.
In a statement, Humberside Police said: “A 24-year-old man has been arrested in connection with the disappearance of Hull student Libby Squire.
“Officers made the arrest at an address in Raglan Street, Hull, last night. The man remains in our custody, assisting us with our enquires.
“We have not yet found Libby and doing so remains our top priority.
“Libby’s parents have been informed of the man’s arrest and we’re continuing to support them at this difficult time.”
A woman, who did not want to be named, said earlier this week that she had heard an “urgent, panicked scream” outside her house at around 12.30am on Friday.
The woman, who lives near Miss Squire’s home, said the area is populated by students who make a lot of noise “any day of the week”.
But she said the nature of the scream she heard on Friday morning was unusual and sounded like a woman was “being harassed”.
She said the scream was followed by male voices and the sound of a “bang”.
She said: “It was an urgent scream. It was panicked. It sounded like she was being harassed. That’s not unusual but not that kind of scream.”
She said she had spoken to police about what she had heard.
This story is being updated