Kardashian’s lawsuit claims that the use of the model has violated her intellectual property rights by using her likeness to promote Old Navy products.
Gap enlisted model Melissa Molinaro for the Old Navy print and TV ads, and then proceeded to tweet about reports that she bore a resemblance to Kardashian.
Kardashian’s lawyers are reported to be seeking about $20m (£12.3m) in damages.
A statement from her legal team says: “Kim Kardashian is immediately recognisable, and is known for her look and style. Her identity and persona are valuable. When her intellectual property rights are violated, she intends to enforce them.”
Kardashian will hope to repeat the success of celebrity lawsuits such as Bette Midler’s case against Ford Motors, which successfully prevented the car marque from using a soundalike to voice one of its TV adverts.
Gap did not respond to a request for comment in time for publication.