Ten people, including four police officers, were wounded in the attack. All of the four attackers are dead and their identities are being investigated, CNN reported.
This is the second attack reported in the past 24 hours.
On May 13, a family including their four children carried out suicide attacks on three churches in Surabaya, killing at least five people and injuring many others.
The attackers included two daughters aged 9 and 12 years old. All of the six bombers died.
It is believed that the parents belong to Jamaah Ansharut Daulah, a terrorist group that supports Islamic State of Iraq and Syria (ISIS) in Indonesia.
The ISIS claimed responsibility for what it called "martyrdom attacks" in the port city on the east coast of Java Island, through its Amaq News Agency. But they didn't provide any proof to substantiate its claim.
The claim is not yet confirmed by the authorities.
Indonesia is the world's most populous Muslim country which has been struggling with a rise in Islamist militancy. (ANI)