Frankin’s book that pokes fun at the network and host Bill O’Reilly. Fox had charged in the suit that Mr Franken had violated its trademarked phrase “Fair and Balanced” through the title of his book, Lies and the Lying Liars Who Tell Them: A Fair and Balanced Look at the Right.
Fox is owned by News Corporation and Penguin is a unit of education and publishing conglomerate Pearson.
The book went on sale last Thursday.
On Friday US District Judge Denny Chin had slammed the network’s request for an injunction aimed at stopping future sales of the book.
He said Fox’s motion seeking the order was “wholly without merit”.
The judge also said he thought it ironic a media company that should be fighting to protect free speech would seek to undermine the First Amendment, which guarantees freedom of speech and of the press.
When asked to comment on its decision to drop the case, a Fox spokeswoman said: “It’s time to return Al Franken back to the normal obscurity he’s accustomed to.”
Floyd Abrams, a lawyer for Mr Franken and Penguin, said he received court papers from Fox saying it had dropped the case. “The decision by Fox is welcome if overdue,” Mr Abrams said. “The suit never should have been brought.”
Fox argued during a hearing on Friday that the subtitle “A Fair and Balanced Look at the Right”, featured on the cover, could confuse consumers who might think either Fox or Mr O’Reilly were sponsoring the book.
But Mr Chin pointed out the word “Lies”, in the title, is printed in large red letters next to a photo of Mr O’Reilly. He said there was no likelihood book buyers would be misled.
Mr Chin also said there was no evidence of bad faith by Mr Franken to mislead consumers into thinking he works for Fox. “There is no intent by Mr Franken to palm himself off as a Fox commentator,” he said.