Police said one or two suicide bombers had targeted people leaving a service for Palm Sunday, the first day of Easter.
There were body parts at the scene, police told media, but they had yet to be identified.
Militant Islamists have attacked churches in the past but no group has yet said it was behind the bombing.
A priest at the church, Father Wilhemus Tulak, told Metro TV that security guards had tackled one suspected bomber.
The attacker, he said, arrived by motorbike and tried to get into the church.
The priest added that some of the victims suffered serious injuries.
The blast happened by the church’s side entrance. Footage from security cameras showed fire, smoke and debris being blown into the middle of the road.
Makassar Mayor Danny Pomanto said that if the explosion had happened at the main entrance, it could have led to far more casualties.
Gomar Gultom, head of the Indonesian Council of Churches, said the attack on people celebrating Palm Sunday was “cruel”.
He urged people to stay calm and trust the authorities.
Churches have been targeted in the past by extremists in Indonesia, the world’s biggest Muslim-majority nation.
In 2018, dozens of people were killed in bomb attacks on churches and a police headquarters in the port city of Surabaya.
Police blamed an Islamic State-inspired network, the Jamaah Ansharut Daulah (JAD) group, for the attacks.
The South East Asian country has long struggled with Islamist militancy. Indonesia’s worst ever terror attack was in Bali in 2002, when 202 people – mostly foreigners – were killed in an attack on a tourist nightlife district.
That attack was carried out by the Jemaah Islamiah (JI) militant network and prompted a sustained crackdown on militants.