The police said an eight-year-old girl from the family survived, while her mother, father and two brothers died. Ten others were reportedly injured.
The blast appeared to be a copycat of a series of devastating bombings at three churches on Sunday morning, in which a mother and father used their young children as cover to murder worshippers.
The mother Puji Kuswati (42) tried to force her way into the Indonesia Christian Church with her two daughters, aged 12 and nine, and triggered an explosive when she was stopped by security.
The father, Dita Oepriarto, (45) drove a car bomb at another church target, while his two teenage sons, 18 and 16, rode an explosives-laden motorbike into a crowd outside a third place of worship. All six family members died
In a separate incident on Sunday, a man acquainted with Dita detonated an explosive as police closed in on his apartment, killing his wife and one of his children and injuring another three.
The serial bombings have revived fears about radicalisation in the world’s most populous Muslim nation and of possible attempts by Isil to spread its influence in Southeast Asia after the crushing of its fledgling caliphate in the Middle East.
Hundreds of Indonesians have flocked to Syria and Iraq in recent years to join Isil forces, raising fears they could regroup when they return home.
The police corrected their initial claims that the family had returned from Isil-controlled Syria but said the father was a local leader of the extremist network Jamaah Ansharut Daulah (JAD) which supports Isil.
The terrorist group immediately claimed responsibility although there is no evidence they co-ordinated the attack from outside the country