Shootout at Indonesia's national police headquarters: media
Major TV broadcasters aired images that showed what appeared to be a person wearing a veil and long black clothes entering the complex as gunshots rang out.
The lone figure fell to the ground and lay motionless afterward as police surrounded the body, the images showed.
Police outposts have also been frequent targets of Indonesian extremists in the past.
Authorities did not respond to a request for comment.
Several of the wounded were in intensive care for serious burns.
The newlywed couple who attacked the church Sunday belonged to pro-Islamic State extremist group Jamaah Ansharut Daulah (JAD), police have said, warning of more possible attacks.
More than a dozen others suspected in the plot have been arrested in recent days.
The couple belonged to an Islamic study group along with several of the other suspects, police said.
Sunday's explosion at the main Catholic cathedral in Makassar took place just after congregants finished celebrating Palm Sunday, the first day of Holy Week in the run-up to Easter Sunday.
The attack came after the arrest of dozens of suspected militants in recent months by Indonesia's counter-terror squad.
The world's most populous Muslim-majority country has long struggled with Islamist militancy and has suffered a number of devastating attacks in the past two decades.
The 2002 Bali bombings were the country's worst-ever terror attack, killing more than 200 people, mainly foreign tourists.
Indonesia's security forces regularly arrest suspected militants and attacks have often been low-level and have targeted domestic security forces.
Before Sunday, one of the country's last major deadly attacks was in 2018, when a dozen people were killed after a family of suicide bombers blew themselves up at churches during Sunday services in Indonesia's second-biggest city Surabaya.
The family -- including two daughters, aged nine and 12 -- and another family of five, which carried out the suicide bombing of a police headquarters, all belonged to the same Koran study group and were linked to JAD, which has pledged allegiance to the so-called Islamic State.
Formed in 2015, JAD gained notoriety the following year for a gun and suicide bomb attack in the capital Jakarta that killed four civilians and four attackers -- including one who blew himself up at a Starbucks outlet.
It was the first attack claimed by IS in Southeast Asia.
JAD was also implicated in a 2019 cathedral suicide bombing in the Philippines committed by a married Indonesian couple which killed worshippers and security forces.