Police, coastguards and mountain rescue teams are looking for Constanze Czerwinske who was on a coastal walk near the village of Glencolmcille.
Ms Czerwinske, who was travelling alone, told other backpackers she was going walking.
She failed to return to the hostel where she had left her belongings and the alarm was raised.
There are fears she could have been swept out to sea or fallen from the nearby Slieve League cliffs on the Atlantic coast.
A spokeswoman for the Irish police force, An Garda Siochana, said bad weather could hamper Friday's search efforts.
Fifteen search teams, made up of a total of 60 police and local residents, have been concentrating on a stretch of coastline between Port and Silver Strands.
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