The crudely made film, called Innocence of Muslims, sparked protests across the Muslim world.
Leaving the video on the website violated the rights of an actress who sued after she said her performance for another movie was edited into in Innocence of Muslims, and her voice was dubbed, a federal appeals court in San Francisco ruled.
Google's argument that having to take down the video would violate the company's free-speech rights was rejected in a 2-1 decision by the court, according to the report.
The court agreed with the actress, Cindy Lee Garcia, that the video needed to be taken off YouTube in part because of ongoing death threats against her, according to the paper.
Garcia had sued Google after failing to convince the company to takedown the video from YouTube, the paper said.
"I am a strong believer and supporter of the First Amendment and have the right not to be associated with this hateful speech against my will," Garcia said in a statement published by the paper.
DPA