Several motorbikes were also damaged in the explosion in the parking lot of the Oikumene Church in Samarinda, the provincial capital of East Kalimantan province, said national police spokesman Maj Gen Boy Rafli Amar.
The children, aged 2 to 4 years old, suffered burn injuries, Amar said.
Media reports cited local police spokesman Lt Col Fajar Setiawan as saying the explosion came from a Molotov cocktail thrown by a man riding on a motorbike.
The man jumped into a nearby river but was captured by locals and handed over to police. TV footage showed the injured man lying on the deck of a motorboat. He was wearing a black shirt with the words "Jihad, Way of Life."
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He moved to East Kalimantan about a year ago.
It was the second explosion at a church in Indonesia this year.
In August, a would-be suicide bomber failed to detonate a bomb during a Sunday Mass in a church in Medan, the provincial capital of North Sumatra in western Indonesia, but he managed to injure a priest with an axe before being restrained.
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