Division bench of Justices S A Bobade and Rajesh Ketkar today sought replies of the respondents in two weeks.
The other respondents to the PIL include Union Ministry of Information and Broadcasting and Google Inc.
The film, made in USA, recently sparked off violent protests in the middle-east and also in Pakistan.
The PIL, filed by local Congress member Ameen Mustafa Idrisi, also demands criminal action against top officers of Google for letting the film that has "hurt the religious feelings" of Muslims across the world to be online.
It seeks action against Google and YouTube under the relevant sections of Indian Penal Code and Information Technology Act, 2000, said petitioner's lawyer Ejaz Naqvi.
Also, the non-Muslim cast and crew of the "outrageous and offensive film" should be booked for insulting the Prophet Mohammed, the petition says.
If the film is not removed from the search engines, serious law and order problems could arise, it says.