Ambulances and the bomb squad descended on the chaotic scene as the 10 injured people included six civilians and four police men.
The suicide bombing took place at three churches in Surabaya, Indonesia's second biggest business city after Jakarta, nearly simultaneously yesterday morning. Police also reported that Sunday evening, a mother and her teenage daughter were killed in a Surabaya suburb when a bomb being handled by the family's father prematurely went off, CNN reported.
Indonesian President Joko Widodo ordered a full investigation into the roots of the organisation blamed for the three church bombings.
Experts on militant networks have warned for several years that the estimated 1,100 Indonesians who travelled to Syria to join IS posed a threat if they returned home.
The Islamic State (known as ISIS) claimed responsibility for the church attacks. Three suicide blasts were committed by one family - a husband, wife and four children - against three churches in the town.
The father of the church suicide bombers was a local leader in extremist network Jamaah Ansharut Daulah (JAD), which supports IS.
That blast killed three people - a couple and their eldest son, 17 - and seriously injured two of their three other children. "The attacks yesterday are part of a pattern ... but (are among) the more sophisticated, and as it involved children, heinous".
Jemaah Islamiyah, the network responsible for the Bali attacks, was obliterated by a sustained crackdown on militants by Indonesia's counterterrorism police with USA and Australian support.
The coordinated bombings on Sunday, followed on Monday by a suicide attack by another family on police headquarters in Surabaya, have horrified Indonesians who typically see their Muslim-majority country as diverse and tolerant.
Kuswati, with her two daughters, attacked the Christian Church of Diponegoro, he said.
"We are still looking, they are being pursued by our colleagues in the field", said East Java Police Chief Machfud Arifin at a press conference in Surabaya today as quoted by Detik.
Police said they also shot dead four suspects, including the second-ranking member of the JAD cell in Surabaya, in raids on houses and offices Monday while nine others were arrested.
Surabaya is the second-largest city in Indonesia, according to the BBC.