The U.S. District Court lawsuit, which was filed Thursday, said the show, which airs on the Fox broadcast television network, didn't have the 73-year-old comedian's permission to include her cleaning woman character, Charwoman, in an April 2006 episode.
The episode shows Charwoman as a porno-shop maid, and it uses what the lawsuit called an "altered version" of Burnett's theme music.
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The characters in the show also perform Burnett's signature ear tug, the lawsuit said.
Besides copyright infringement, Burnett alleges 20th Century Fox violated her publicity rights.
The studio said it was surprised by the lawsuit over what amounted to about an 18-second scene.
"'Family Guy,' like 'The Carol Burnett Show,' is famous for its pop culture parodies and satirical jabs at celebrities. We are surprised that Ms. Burnett, who has made a career of spoofing others on television, would go so far as to sue 'Family Guy' for a simple bit of comedy," said 20th Century Fox Television spokesman Chris Alexander.
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