Scotland's animal welfare charity The Scottish SPCA was alerted after the theft at a farm in Newbigging, which occurred between the night of Tuesday, April 1 night and the following morning.
A young male goat aged under a year old was also taken.
Chief Inspector Paul Anderson said, "There are clear welfare concerns for these goats if the thief does not know or understand their needs.
"It's also very worrying that a mother has been taken away from her kid far too soon and this will undoubtedly have resulted in a great deal of distress for them both.
"The female is an adult Guernsey goat and the young male is white with a brown neck and red paint mark on his tail.
"As she is so young, the kid, named Daffodil, is now having to be bottle fed round the clock by her owner.
"We are very keen to reunite Daffodil with her mother as soon as possible.
"If anyone has any information we would urge them to contact our animal helpline on 03000 999 999 or Police Scotland immediately."