New York (CNN) A patient at a southern New Jersey hospital inadvertently got a transplanted kidney that was intended for another patient, officials confirmed to CNN Tuesday.

The 51-year-old patient was on the transplant list at Virtua Our Lady of Lourdes Hospital, but a day after the transplant someone on the clinical team realized the patient "was inadvertently transplanted out of priority order," according to a press release from the hospital.

The hospital notified the patients in the case, and the patient who was supposed to get the kidney received one six days later. Both patients are doing well, the hospital confirmed. Neither patient was identified by the hospital.

The hospital also reported the incident to the Organ Procurement and Transplantation Network and the New Jersey Department of Health, who investigated the incident, according to the hospital.

"We have a profound responsibility to people who literally place their lives in our hands," said Dr. Reginald Blaber, executive vice president and chief clinical officer of Virtua Health. "Mistakes of this magnitude are rare, and despite the unusual circumstances of similar patient identities, additional verification would have prevented this error."

Read More