Semiofficial news agency ISNA quotes Ruhollah Momen Nasab, an official with the paramilitary Basij force, as saying Tuesday that the judge also ordered the two apps blocked.
Another Iranian court last week had ordered Instagram blocked over privacy concerns. However, users in the capital, Tehran, still could access both applications around noon Tuesday. In Iran, websites and Internet applications have sometimes been reported blocked but remained operational.
Facebook is already banned in the country, along with other social websites like Twitter and YouTube.
The administration of moderate President Hassan Rouhani is opposed to blocking such websites, just last week, in a speech, he said that "We ought to see (the Internet) as an opportunity. We must recognise our citizens' right to connect to the World Wide Web," said Rouhani according to the official IRNA news agency.
"Why are we so shaky? Why have we cowered in a corner, grabbing onto a shield and a wooden sword, lest we take a bullet in this culture war?" he said in his weekend speech.
"Even if there is an onslaught, which there is, the way to face it is via modern means, not passive and cowardly methods."
Iran has long had a contradictory attitude towards the Internet. Access to sites like Twitter, Facebook and Youtube is blocked for most Iranians, but Khamenei himself joined Twitter and Facebook in 2009 and is now a prolific user of both.
These days the Supreme Leader often sends out more than a dozen tweets a day in English, Farsi and Arabic. His latest informed his 53,900 followers that "Despite industrial progress in the #West, negligence & humiliation of #family & its values will cause West to collapse in the long run."
On his Facebook page, where he has 82,000 "likes", Khamenei offers spiritual guidance, telling those seeking a spouse to accept compromise: "a perfect flawless wife or a perfect flawless husband cannot be found anywhere in the world."
Yet Abdolsamad Khoramabadi, secretary of a state committee tasked with monitoring and filtering sites, last year called Facebook a US espionage project.
Iran's leadership cracked down hard against Internet users in 2009 following Ahmadinejad's disputed 2009 re-election that year, when a violent crackdown on street protests led to the worst unrest in the Islamic Republic's history.
Many bloggers were jailed and at least one person was sentenced to death for running a website seen by the authorities as subversive.
Reuters contributed to this report