The communications ministry said in a statement that "so many channels in the (Telegram) service contain radicalism and terrorism... encouragement and tips to assemble bombs or launch attacks" that it needed to block it.
The partial ban came as the country suffered from a string of attacks, including one carried out by a man police said was radicalised after reading radical material on Telegram.
The government has so far bocked only access to the app via computer, but is preparing to impose a full ban.
"We are now preparing a process to close down Telegram app in full throughout Indonesia if Telegram does not come up with a standard operating procedure to handle law-violating contents," the communications ministry said in a statement issued late Friday.
In June, a lone wolf attacker stabbed two police officers in a mosque. Police said the man had no links to militant groups but had been radicalised through material he read on Telegram.
Telegram is a free Russian-designed messaging app that lets people exchange messages, photos and videos in groups of up to 5,000. It has attracted about 100 million users since its launch in 2013.
The app has come under fire in Russia after the state communications watchdog threatened to ban it in June, saying the company behind the service had failed to submit company details for registration.
Russia's FSB security agency also said Telegram was used by those behind April's Saint Petersburg metro bombing.
Telegram CEO, Pavel Durov, said the firm will investigate the Indonesia charges.
"We have never received any requests/complaints from the Indonesian government," Durov said on Twitter.
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