The attack happened at around 7.30pm last night at a house on the Lough Road in Milford.
The woman was taken to hospital but her injuries are not understood to be life-threatening.
A 20 year old man has been arrested and is being questioned under the Criminal Justice Act.
It is still unclear as to the circumstances surrounding the attack.
It is understood the young woman’s attacker is known to her.
“This is a dreadful incident,” said one local man, “the victim is a young girl; she’s still a teenager.
“Everyone around here is praying for her this morning. We hope she is OK.”
It’s the latest stabbing incident in Co Donegal following recent incidents in Letterkenny.