The 24-year-old was held last night less than a mile from where the 21-year-old was last seen sat on a park bench six days ago.
A car was last night removed from Raglan Street where the suspect was held as forensic officers were seen going in and out of the home.
Cops confirmed this morning he has been arrested on suspicion of abduction.
In a statement, Humberside Police said: "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."
THE LAST SIGHTINGS OF LIBBY
11pm Thursday January 31: Libby is refused entry at Welly Club, Beverley Road, 4kms from her home. The student was put into a taxi home.
11.30pm: Libby was seen staggering around outside her student digs on Wellesley Ave
11.45pm: CCTV captures Libby sitting on a bench on Beverley Road, close to the junction of Haworth Street.
She was also helped by a motorist
12.09am: Police beliee Libby stayed in the area for about half an hour
12.30am: A neighbour hears 'blood-curdling' screams
January 3 midday: Forensic officers find screwdriver, claw hammer and lip gloss 40 yards from where Libby was last seen
January 6: A 24-year-old man is arrested in connection with the disappearance less than a mile from Libby's home
A huge search was launched with cops searching a river and pond close to her university home in Hull, East Yorks, but no trace of Libby has been found.
Bins, drains and gardens were also combed by officers but searches have so far proved fruitless.
Her parents, Lisa, 48, and Russell, 53, have now travelled from the family home in High Wycombe, Bucks, to Hull.
The couple visited her home on Wellesley Avenue in the city – close to the University – and walked around the area where she was last seen.
'SNATCH' FEARS
Desperate pals yesterday spoke of their fears the philosophy and religion student may have been snatched.
One said: “It’s always been in our minds. How could it not? The longer it goes on the more we are worrying.
"The police have searched the local river, the pond, they've searched gardens, bins, drains and she's still nowhere to be seen."
Friend Lauren Goodman said: “Libby has always got to a phone or made sure someone knows she is safe. To not hear from her at all is completely not like her.”
Another pal Chloe Wise said: "Libby is still out there somewhere. Please if you know anything at all don’t hesitate to contact police."
'BLOOD-CURDLING SCREAMS'
It comes after a horrified neighbour revealed she heard a woman’s "blood-curdling" screams at 12.30am last Friday.
The resident said the terrified high-pitched cry was loud enough to make her sit up in bed and yell "oh my god".
Just 45 minutes earlier, Libby was captured on CCTV 100 yards away sat on a bench near her student digs.
She had earlier been put in a taxi by pals after she was turned away from the Welly Club at 11pm on Thursday.
She was then seen staggering and falling over outside her house.
She was wearing a black long sleeved top, leather jacket and black denim skirt with lace and had been drinking heavily.
Police found lip gloss, a screwdriver and a hammer in a hedge close to where she was last seen but it was not known if they are connected to the case.
PARENTS' ANGUISH
Libby’s parents Lisa and Russell made an emotional video appeal for help in finding their daughter.
Lisa, 48, said: “Libby, my darling pie. We just want to know that you are safe.
“The whole family is missing you, especially me and your dad, sisters and brother.
"It is breaking my heart not knowing where you are. I love you more.”
Russell, 53, added: “Libby is our kind, thoughtful, beautiful girl. We just want her home.”
More to follow…
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