Surabaya: Two militants on a motorcycle blew themselves up at a police headquarters in Indonesia's second biggest city Surabaya on Monday claiming at least one police casualty, authorities said, just a day after a wave of suicide bombings on churches killed at least 14 and injured dozens.

Citing CCTV footage from the scene, East Java Police spokesman Frans Barung Mangera said a man and a woman on the bike stopped at the security checkpoint.

"That's where the explosion happened," he added.

"Two people were riding (on the motorcycle) and a woman was sitting at the back." Authorities did not immediately say if the police officer at the checkpoint had been killed or injured.

The deadly explosion comes just a day after a family of six including two young daughters staged suicide bombings at three churches in Surabaya during Sunday services.

At least 14 have died as a result of that attack, which was claimed by the Islamic State group, and the toll could climb with more than 40 injured in hospital.

The church bombers -- a mother and father, two daughters aged nine and 12, and two sons aged 16 and 18 -- were linked to local extremist network Jamaah Ansharut Daulah (JAD) which supports IS, police have said.

A further three people in one family were killed and two wounded when another bomb exploded at an apartment complex about 30 kilometres from Surabaya, just hours later, police said.

The mother and one child died from the explosion while police said they shot dead the father who was carrying a bomb detonator.

Two other children were injured in the blast and were taken to hospital. There was no immediate claim of responsibility for the apartment bomb.