National police spokesman Anton Charliyan said it was not clear yet which group had carried out what the Indonesian president has termed "acts of terror".
But he said that IS issued a cryptic warning before the attacks.
"The warning said there will be a concert in Indonesia and it will be international news," he told a local radio station.
He did not give any further details, or say when the warning was issued.
Police foiled several terror plots in Indonesia last month, with some believed to be linked to IS.
Hundreds of Indonesians are feared to have joined the jihadist group, which has taken over vast swathes of territory in Iraq and Syria.
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