Actress Cindy Lee Garcia had sought to have the film removed in a suit against YouTube parent company Google Inc and a California man linked to the film, saying she was duped into taking part and had since received death threats.
"The request for a temporary restraining order is denied. The plaintiff has not shown a likelihood to prevail on the merits," Los Angeles Superior Court Judge Luis Lavin said.
Garcia's is the first known civil lawsuit connected to the making of the video, which depicts the Prophet Mohammad as a womanizer and a fool, and which helped generate a torrent of violence across the Muslim world last week, the anniversary of the September 11, 2001, attacks on the United States.
The violence included an attack on U.S. diplomatic facilities in Benghazi in which the U.S. ambassador to Libya and three other Americans were killed. U.S. and other foreign embassies were also stormed in cities in Asia, Africa and the Middle East by furious Muslims.
Garcia accused a producer of the movie, whom she identified as Nakoula Basseley Nakoula using the alias Sam Bacile, of duping her into appearing in a "hateful" film that she had been led to believe was a simple desert adventure movie.
"There was no mention of 'Mohammed' during filming or on set. There were no references made to religion nor was there any sexual content of which Ms. Garcia was aware," the lawsuit said.
For many Muslims, any depiction of the prophet is blasphemous. Caricatures deemed insulting in the past have provoked protests and drawn condemnation from officials, preachers, ordinary Muslims and many Christians.
Garcia, who said she had received death threats after the video was posted on YouTube, has accused Nakoula of fraud and slander.
Garcia also named Google and its YouTube unit as defendants in the suit she filed on Wednesday. She said her right to privacy had been violated and her life endangered, among other allegations.
An attorney for Google said the rights of an actor do not protect that person from how a film is perceived.
"If we viewed it that way we'd say that Arnold Schwarzenegger as a cyborg in 'Terminator' was a factual statement about Arnold Schwarzenegger," lawyer Timothy Alger said.