The incident happened on Friday.
The family of a person who died from Covid-19 was given the wrong body by a hospital mortuary last weekend.
The incident happened at Mullingar Regional Hospital on April 24th.
A full internal review is now being carried out into the incident at the mortuary of Mullingar Regional Hospital.
In a statement, the Ireland East Hospital Group, which operates the facility, says a mistake resulted in the release of incorrect remains to an undertaker.
It says once detected, the issue was rectified.
Victims of Covid-19 are put in sealed bodybags by morticians due to the nature of the disease, with neither families or undertakers allowed to view the remains.
The hospital group has apologised for the distress the incident caused to the families involved, describing it as an "extremely rare event."