West Mercia Police said officers were called to HMP Long Lartin in South Littleton, Worcestershire, shortly after 10am on Friday morning.
The 25-year-old “sustained serious injuries and was airlifted to hospital,” the force added. They are still in hospital, but in a stable condition.
A 22-year-old suspect is being held in custody within the prison, and a weapon has been recovered, the force said.
In a follow-up statement, the police said audio footage circulating online, and claiming to be from the aftermath, is not connected to the incident.
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Assistant Chief Constable Grant Wills said: “Whilst our investigation is in its early stages, we would like to clarify that this incident is not being treated as terrorism.
“Our initial enquiries suggest there was a disagreement between an inmate and prison officer that escalated and is an isolated matter within the prison.”
HMP Long Lartin is category A and category B prison with space for over 600 inmates.
