Susilo Bambang Yudhoyono said the scale of the slaughter wrought by the extremists in overrunning large swathes of Iraq and Syria and the level of violence being used was appalling.
"It is shocking. It is becoming out of control," he said in an interview with The Australian, a day after IS released a video showing a masked militant beheading US reporter James Foley, provoking worldwide revulsion.
"We do not tolerate it, we forbid ISIS in Indonesia," he added, referring to the Islamic State of Iraq and the Levant, as IS was formerly known.
He asked international leaders to work together to combat radicalisation.
"This is a new wake-up call to international leaders all over the world, including Islamic leaders," he said, adding that the actions of IS were not only "embarrassing" to Islam but "humiliating", the newspaper reported.
"All leaders must review how to combat extremism. Changing paradigms on both sides are needed - how the West perceives Islam and how Islam perceives the West."
Indonesia is home to the world's biggest Muslim population of about 225 million and has long struggled with terrorism. But a successful clampdown in recent years has seen the end of major deadly attacks.
"Our citizens here in Indonesia are picking up recruitment messages from ISIS containing extremist ideas," said the president, whose decade in office comes to an end in October.
"The philosophy of ISIS stands against the fundamental values we embrace in Indonesia. Last Friday, in my state of the union address to the nation, I called on all Indonesians to reject ISIS and to stop the spread of its radical ideology.
