The graveyard was cordoned off at Annagry, a Gaeltacht village in the west of the county, during the investigation.
Gardaí arrived at around 6am and placed a large black forensic tent around a grave. A small coffin was moved as part of the operation and it was first understood to contain the remains of a child who died within the past 18 months.
Arrangements had been made for it to be taken to Letterkenny General Hospital for a full examination.
However, shortly after the coffin was raised speculation arose that the coffin may not contain any remains at all — human or otherwise.
A number of people attempting to visit the graveyard were asked to remain outside while the examination took place.
The details of what led to the exhumation taking place were unclear.
A Garda spokesman confirmed an exhumation had taken place but said they could not comment further because of operational matters.
He said the exhumation was taking place between gardaí and the coroner for the north-west of Donegal.
A local Garda source also confirmed the operation to remove a coffin had taken place but described the situation as “sensitive”.
The tent was brought down after the coffin was taken away, and people were allowed back into the graveyard after 2pm yesterday.
A local resident said: “Nobody really knows what has happened. The grave which was examined belongs to that of a couple from outside the area who had lived here for a while.
“They did lose a baby but nobody knows why the coffin has been dug up.”