They were playing in the parking area of the church on Indonesia's Borneo island when the man threw the bombs from his motorbike.
It was the latest attack in the world's most populous Muslim-majority country against a minority group in Indonesia, which is home to significant numbers of Christians, Hindus and Buddhists.
"The man passed by the church and threw what we suspected was low-explosive cocktail bombs, causing light injuries on four children who were playing there," local police spokesman Fajar Setiawan told AFP.
The attacker, who was wearing a t-shirt emblazoned with the word "jihad", has been captured and an investigation is underway, police said.
The motive of the attack was still unclear, Setiawan said, but the churchas well as a mosque where the man went before the incident had been cordoned off for the investigation.
In August, an Indonesian teenager who was obsessed with the Islamic State group stabbed a priest in a church and tried to detonate a homemade bomb.
In July an IS-linked suicide bomber targeted a police station on Java island, causing minor injuries to one officer.
A suicide bombing and gun attack in the Indonesian capital in January, claimed by IS, killed four attackers and four civilians.
