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The actress will play a stay-at-home mother in an upcoming episode of the drama, TV Guide reports.
Her character will reportedly be talking to her travelling husband on a webcam when she is attacked and kidnapped.
Sevigny, who will allegedly begin filming her episode next week, previously played Nicolette in Big Love. Her movie credits include Zodiac and American Psycho.
She will also appear in the upcoming British drama Hit and Miss, which will air on Sky Atlantic in the UK and on DirecTV in the US.
Miranda Lambert, Harry Connick Jr and Tommy Flanagan are among the other stars who have filmed appearances in this season of Law & Order: SVU.
The show airs on Wednesdays on NBC.
