Mrs Fox tells the story of a woman who turns into a fox to her husband's confusion and dismay.
Frostrup said from the outset of deliberations the judges had all been "seduced by our winning story".
"The poetic use of language, the dexterity and originality of the prose made Sarah Hall's Mrs Fox utterly unique," she said.
Hall has won a growing list of awards for her short stories and four novels and has been selected as one of this year's Granta's Best Young British Novelists.
Speaking about Mrs Fox, she said she was "fascinated by situations in which human beings are challenged and placed outside the usual codes of conduct".
She was previously shortlisted for the BBC short story award in 2010.