The woman was detained by the PSNI on suspicion of misconduct in a public office.
She has since been released on bail.
The prison officer, who has been suspended from duty following an internal investigation, works at Maghaberry high security prison.
It is understood the alleged relationship was with a convicted killer.
The pair are believed to have worked together in the prison’s kitchen.
The prisoner involved is reported to be Robert Young from Portadown.
He was jailed in 2005 for the murder of drug dealer Jim Johnston outside his home at Crawfordsburn in County Down.
Jailing Young for a minimum of 22 years, the judge at that time said he had shown “supreme indifference” to both the murder and his conviction.
He said Young, now 51, was guilty of a “cold-blooded, callous murder”.
A Prison Service spokeswoman said: “The Northern Ireland Prison Service can confirm that a member of staff has been suspended following an internal investigation.
“This is now a matter for the PSNI and it would be inappropriate to comment further.”
A PSNI spokesman said: “PSNI have arrested a female on suspicion of misconduct in a public office.”