A video of the scene showed the girl staggering through the rubble before a bystander picked her up and carried her to safety. The trio went inside and detonated a bomb.
The sons aged 16 and 18 rode a motorcycle onto the grounds of the Santa Maria Church and detonated their explosives there, he said.
Daesh has claimed responsibility for the church bombings. "When we searched the flat we found pipe bombs, similar to pipe bombs we found near the churches", said Karnavian.
Indonesia has been on high alert for attacks by homegrown militants, including some claimed by ISIS.
Police said they arrived after the explosion and shot dead the injured man, Anton Febrianto, as he held a bomb detonator in his hand.
Anton died later after police officers gunned him down to prevent him from triggering another bomb.
Police clashed with rioting inmates at the facility near Jakarta last Tuesday.
It also advised Singaporeans in Indonesia to let their families and friends know that they are safe, as well as e-register with the ministry.
"Then in 2014 there was an uptick in violence as groups linked to ISIS became active, stoked by online propaganda, militants who traveled to the Middle East and fighting in the Philippines", he continued. It didn't mention anything about families or children taking part and said there were only three attackers. Jihadists typically see the Ramadan season as a time in which Allah looks upon terrorist attacks with particular favor.
Indonesia, which is set to host the Asian Games in just three months, has long struggled with Islamist militancy, including the 2002 Bali bombings that killed over 200 people - mostly foreign tourists - in the country's worst-ever terror attack.
Home Affairs Minister Peter Dutton says the use of children in both attacks is barbaric.
The statement issued Sunday offered condolences to the families of victims and said the United Nations stands by Indonesia's efforts to fight extremism and prevent terrorism. Nearly 10% of the population is Christian.
This story has been corrected to reflect new police information on the ages of two of the girls involved in the bombings. His name is Dita Oepriarto.