A judge in Tehran gave "the order to interrupt Telegram", the judiciary's Mizan Online news agency said.
The move comes on the heels of a recent presidential directive banning all government workers from using foreign messenger apps to communicate.
Telegram, built by Russian tech guru Pavel Durov, is the most popular social network in Iran with some 40 million users - roughly half the population.
During a wave of protests that hit dozens of Iranian cities at the start of the year, authorities temporarily banned Telegram, saying the service enabled foreign-based "counter-revolutionary" groups to stir tensions.
Since then, authorities have sought to develop Iranian social media networks and limit the reliance on foreign-based platforms, which Tehran accuses of hosting sites deemed hostile to the Islamic Republic.
Several Iranian platforms offering services similar to Telegram have emerged in recent months, like the Soroush network, which already claims to have five million subscribers.
Iran's supreme leader Ayatollah Ali Khamenei and President Hassan Rouhani both announced in mid-April they would stop using Telegram.
The last message on Khamenei's Telegram channel directed users to accounts on Iranian messaging services, including Soroush and Gap.
The tribunal in Tehran issued its order Monday after receiving complaints against Telegram, accusing it of "inciting rebellion" and allowing "terrorist groups" to threaten national security, Mizan Online reported.
All internet providers and phone operators now have "a duty to completely block access to Telegram," the news agency said, citing the judge's decision
Anyone in breach of the order "will be considered in violation with the judicial order and prosecuted", the news agency said.
AFP journalists said Telegram was still working by Monday evening.