The congregation had been inside the church on the island of Sulawesi at the time of the explosion and the lone attacker was the only fatality, police said.
Father Wilhemus Tulak, a priest at the church, told Indonesian media that the suspected bomber tried to enter the church grounds on a motorbike, but had been stopped by a security guard.
Security camera footage showed a blast that blew flame, smoke and debris into the middle of the road.
Police did not say who might be responsible for the apparent attack and there was no immediate claim of responsibility.
Police blamed the Islamic State-inspired Jamaah Ansharut Daulah (JAD) group for suicide attacks in 2018 on churches and a police post in the city of Surabaya that killed over 30 people.
Boy Rafli Amar, the head of the country's National Counterterrorism Agency, described Sunday's attack as an act of terrorism.
Makassar Mayor Danny Pomanto said the blast could have caused far more casualties if it had taken place at the church's main gate instead of a side entrance.
Makassar, Sulawesi's biggest city, reflects the religious makeup of Indonesia, the world's largest Muslim-majority country with a substantial Christian minority and followers of other religions.
"Whatever the motive is, this act isn't justified by any religion because it harms not just one person but others, too," Yaqut Cholil Qoumas, Indonesia's religious affairs minister, said in a statement.
Gomar Gultom, head of the Indonesian Council of Churches, described the attack as a "cruel incident" as Christians were celebrating Palm Sunday, and urged people to remain calm and trust the authorities.
Indonesia's deadliest Islamist militant attack took place on the tourist island of Bali in 2002, when bombers killed 202 people, most of them foreign tourists.
In subsequent years, security forces in Indonesia scored some major successes in tackling militancy, but more recently there has been a resurgence of militant violence.
