The Ministry of Justice said the initiative is designed to tackle the levels of knife-related incidents at HMP Swaleside, a category B men's prison that holds 1,100 violent offenders.
Sky News has obtained a letter written by Governor Mark Icke pleading with inmates to hand in their improvised weapons.
During the amnesty, which was held in March, Mr Icke told inmates: "No information will be collected to determine who has provided the improvised weapon and there will be no repercussions for anyone who hands over any weapons in the correct way."
The Prison Officers Association has strongly condemned the decision to allow inmates to hand over improvised weapons without fear of prosecution.
The union said it is illegal for inmates to be in possession of an unauthorised weapon and has called for an investigation into why an amnesty was allowed to be held in the first place.
Steve Gillan, general secretary of the POA, said: "I think it is reckless to go ahead with this. It sends the wrong message to prisoners that it is okay to have a weapon. Giving prisoners impunity to hand over weapons which could injure one of my colleagues or another prisoner is just unacceptable."
The Ministry of Justice defended their actions in Swaleside, saying that weapons amnesties are one of the many measures they use to remove illicit items from prisons and reduce violence.
Paul, a former prisoner at HMP Swaleside, told Sky News stabbings were "an everyday reality" and most inmates would carry weapons.
He said: "I have seen axes get made and people getting chased. It is so easy to get a weapon. You can get attacked with batteries in a sock. I have seen people sharpen a soap, put a razor in there and slash someone's face, or they even use paperclips and tie razors around, strap it round someone's neck and try holding them hostage."
The 27-year-old, who spent six years at the prison, said he carried a weapon for his own protection.
"I would carry an ice pick because anything could happen. People would make their own shanks in order to protect themselves."
Government figures analysed by Sky News show 803 weapons have been confiscated from prisoners at HMP Swaleside since 2015 - 45% of those were found in the 12 months to March 2019.
This amounts to almost one a day for the past year.
Swaleside was described as being in a "dangerous" state by the chief inspector of prisons in 2018, with inspectors warning in May that the prison "still suffered high levels of violence and too many men felt unsafe".
Andrea Albutt, president of the Prison Governors Association, said the decision by the governor to hold an amnesty is concerning.
She said: "People carry tools in prisons because they don't feel safe and unless the issues are addressed around safety then holding amnesties are pointless. Prosecuting people for having them in prisons won't make a difference.
"I think amnesties in prisons are a good thing if they are part of a bigger package to address the problems in our justice system."