The government had said it would block access to the entire YouTube website if owners Google did not comply.
Google had rejected a request from the White House to remove the film, but has already blocked access to it in Libya, Egypt, Indonesia and India.
It said it would consider blocks in other nations where the film is illegal
In an official statement, King Abdullah said the website would be blocked if Google did not agree to remove links to the controversial film.
The country's Communications and Information Technology Commission also called on Saudi citizens and expats to report any links they found to the "defaming" film.
"This is considered a duty imposed by our true religion on every Muslim, necessitating the prevention of any blaspheming reports to our Prophet (peace be upon him) and to our true religion," said a statement released via the state press agency SPA.
The Russian government has also asked for the material to be blocked.
A court in Russia is currently considering whether to classify the film as "extremist".
If it is classified as extremist, the entire YouTube website could be blocked.
However, under controversial new legislation due to commence on 1 November, digital content deemed "damaging to children" would be put on a nationwide blacklist and blocked by all internet service providers in the country without the requirement of a court order.
"It sounds like a joke, but because of this video... all of YouTube could be blocked throughout Russia," Russian Communications Minister Nikolai Nikiforov wrote on Twitter.