At least 10 people including police officers were injured in the attack, which the police say, was carried out by a family of five including an eight-year-old-child who survived.
Daesh claimed responsibility for the suicide bombing of a police headquarters in Indonesia's second city Surabaya on Monday, according to the SITE monitoring group.
A family of five, including a child, carried out the suicide bombing which wounded 10 people, police said, a day after a deadly wave of attacks on churches in the same city staged by another family also claimed by Daesh.
"A martyrdom-seeking operation with an explosive-laden motorcycle hit the gate of an Indonesian police headquarters in the city of Surabaya in East Java province in Indonesia," Daesh's official Amaq news agency reported, according to SITE.
On Sunday, a family killed 13 people in suicide attacks on three churches in Surabaya.
The Monday's blast occurred at 8:50 am (0150 GMT), East Java police spokesman Frans Barung Mangera told a briefing.
Citing CCTV footage from the scene, 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."
Mangera said civilians and police were victims of the attack but didn't immediately announce a death or injury toll.
TRT World spoke to Erin Cook in Jakarta for more details.
President condemns "act of cowards"
President Joko Widodo decried the the series of suicide attacks in Surabaya as the "act of cowards", pledging to push through a new anti-terrorism bill to combat networks of militants in the country.
"This is the act of cowards, indignified and barbaric," Widodo said on Metro TV, referring to attacks on three churches in the city on Sunday, as well as outside a police office on Monday.
Widodo said he would issue a regulation in lieu of a law next month to force through a new anti-terrorism bill if parliament failed to pass it.
On Sunday, suicide bombers attacked three churches, killing at least 13 people and wounding about 40.
Police say the family that carried out Sunday's suicide bombings had returned to Indonesia from Syria and included girls aged 9 and 12. All six members of the family died.
Separately on Sunday, three members of another family were killed when homemade bombs exploded at an apartment in Sidoarjo, a town bordering Surabaya, police say.
Indonesia's president condemned Sunday's attacks as "barbaric."
Daesh claim church attacks
Daesh claimed responsibility for the church attacks in a statement carried by its Aamaq news agency. It didn't mention anything about families or children taking part and said there were only three attackers.
Indonesia's deadliest terrorist attack occurred in 2002, when bombs exploded on the tourist island of Bali, killing 202 people in one night, mostly foreigners. But the fact that children were involved in Sunday's attacks in Surabaya shocked and angered the country.
Jemaah Islamiyah, the network responsible for the Bali attacks, was obliterated by a sustained crackdown on militants by Indonesia's counterterrorism police with US and Australian support. A new threat has emerged in recent years, inspired by Daesh attacks abroad.
Experts on militant networks have warned for several years that the estimated 1,100 Indonesians who traveled to Syria to join Daesh posed a threat if they returned home.