The Ministry of Justice (MoJ) said it is "hugely disappointed" by the judge's decision. Former nightclub bouncer Levi Bellfield was attacked by a fellow prisoner with a makeshift weapon in 2009 at Wakefield Prison before he went on trial for the murder of 13-year-old Milly.
He is believed to have suffered minor injuries but launched legal action claiming prison staff should have protected him.
Lawyers on behalf of the MoJ fought against his case for three years but they were forced to admit full liability at Durham County Court on Wednesday.
A Ministry of Justice spokesman said: "We are hugely disappointed Levi Bellfield was awarded £4500 by a judge."