At least 11 people were killed and 41 injured in the attack, which has struck terror into the hearts of Indonesia's sizeable minority Christian community.

The children who participated in the attack were aged nine, 12, 16 and 18 years old and committed the atrocity with their mother and father, according to Indonesian police chief Tito Karnarvian. The two youngest bombers were little girls.

Indonesian President Joko 'Jokowi' Widodo said on Sunday evening that he had instructed police to investigate the network that had carried out the attack.

"All state apparatus will not tolerate this act of cowardice. I ask all people to wage war against terrorism, radicalism that is against religious values, pluralistic values. I also call on all people to remain calm, keep united and stay alert," he said at a press conference after visiting victims in hospital and bombing sites.

The suicide bombers actions were "beyond humanitarian limits", the President said.

The two oldest children, both boys, launched their attacks from motorcycles. The father was in a car, and the mother and two young girls were on foot.

The first attack, at the Santa Maria Roman Catholic Church at about 7.30am on Sunday, killed at least four people including the bomber, according to police.

It was followed soon after by a second explosion at the Christian Church of Diponegoro and then a third at the city's Pantekosta Church, police spokesman Frans Barung Mangera said.

Police have also said that they found and defused an active bomb at the Protestant church, and two more active bombs were found and defused at the Pentecostal church.

Jakarta's terror alert level was raised to the highest level after the bombings on Sunday.

At least 41 people have been confirmed injured and have been admitted to hospital, including two police, following the devastating attacks.

In the hours before the church attacks, national police spokesman Setyo Wasisto announced on Sunday that four suspected terrorists had been killed during a police raid overnight in Cianjur, West Java

Police killed the men after they had produced weapons during the raid and evidence confiscated included revolvers, bullets and an arrow with a bomb placed on the end of it, Wasisto said.

"They have trained in order to attack police," Wasisto said, identifying the militants as members of Jemaah Anshorut Daulah, or JAD.

The network of about two dozen extremist groups has been implicated in a number of attacks in Indonesia over the past year. It pledges allegiance to Islamic State group leader Abu Bakr al-Baghdadi.

The last time there was a coordinated attack like this involving a series of bombs was the second Bali bombing back in 2005. These are the worst bombings of Christian churches since Christmas Eve, 2000, when 15 people were killed.

All other masses in Surabaya scheduled for Sunday were cancelled and Indonesian police are now searching other churches and working to head off any further attack.

Some churches in Surabaya were planning to hold Mass late in the afternoon on Sunday, after being checked by the bomb squad.

The Nahdlatul Ulama (NU), a 50-million-member moderate Islamic organisation that promotes pluralism and tolerance, strongly condemned the attacks "whatever the motive and background".

"All kinds of violent actions, particularly those carried out in the name of religion by way of spreading terror, hatred and violence are not the character of Islam. There is no religion in the world that justify violent actions" the organisation said in a statement.

Nasir Abbas, a former senior member of terrorist group Jemaah Islamiyah who now works with Indonesian police, said he "strongly condemned the suicide bombing in three churches".

"They [the perpetrators] are misguided. My condolences for the victims at the churches."

Christians make up about 9 per cent of the 260 million people who live in the majority-Muslim nation.

The attacks come just days after Islamist militant prisoners killed five members of an elite Indonesian counter-terrorism force, Detachment 88, at a high-security jail in Jakarta and took another officer hostage.

The hostage was eventually released after a 36 hour stand-off. Islamic State claimed responsibility for the attack.

Since that incident, police and public figures have asked that footage of that incident, and of the bombings, not be shared as doing so would please the terrorists involved in the attacks.

Surabaya is Indonesia's second-largest city.

No information about the perpetrators or the victims has been released yet.

with AAP