Two-year-old Intan Olivia Marbun was among four small children hurt when an attacker wearing a t-shirt with the word "jihad" on it threw explosives at the church on Borneo island Sunday from a motorbike.
The youngsters, aged between two and four, had been playing in the car park of the church in the city of Samarinda at the time of the attack.
Local police spokesman Fajar Setiawan told AFP that Marbun suffered severe burn injuries, adding: "Unfortunately the doctors could not save the victim... She died early this morning."
"We hope they can come home soon," said Setiawan.
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Police have arrested the suspected attacker, a 32-year-old man who was previously jailed over his involvement in a parcel bomb plot in 2011 targeting figures including a moderate Muslim cleric and the counter-terror chief.
Indonesia has the world's biggest Muslim population, but most practise a moderate form of Islam and the country is also home to substantial populations of Christians, Buddhists and Hindus.
However there has been an increasing number of attacks on religious minorities in recent years by Muslim hardliners.
The rise of IS has also fanned the flames of extremism in a country that has long struggled with militancy, with hundreds of Indonesians heading to fight with the jihadists in the Middle East.
A suicide bombing and gun attack in the Indonesian capital Jakarta in January, claimed by IS, killed four attackers and four civilians.
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