The remains of the foetus, which is believed to be more than three months into pregnancy, was found yesterday afternoon.
It is still unclear as to how the foetus came to be at the location in which it was found.
It is understood the remains was found in the open and close to a house.
The foetus was found at a townland known as Brenter in Dunkineely.
The foetus was transferred to Letterkenny General Hospital where its age was determined.
Gardai say they are concerned about the welfare of the mother whom they say could need vital medical attention.
Theya have appealed to anybody who knows anything about the situation to come forward or contact Ballyshannon Garda station.
They have stressed that all calls will be treated sensitively.