A spokesman for the national police, Inspector General Argo Yuwono, said the wounded suffered from injuries around their necks, chests, and legs, noting that some had blisters on their hands and feet.
The National Police said the attack could have claimed more lives without intervention by a church security guard.
He said security guards had suspected two motorists who wanted to enter the church and confronted them.
The priest explained that a suspected bomber, who arrived on a motorbike, tried to enter the cathedral but was turned away by security guards.
An eyewitness at the scene described the explosion as "very strong".
Several worshippers nearby were injured by flying glass from shattered windows, Father Wilhelmus noted.
Earlier Sunday, Makassar Mayor Mohammad Ramdhan said: "There are many body parts here at the church compound as well as in the street".
Indonesian President Joko Widodo said he "strongly condemned this act of terror".
"Terrorism is a crime against humanity and has nothing to do with any religion", he declared. General Listyo said the explosion was caused by a pressure cooker bomb.
It comes a week before Easter.
An explosion occurred outside a Catholic church in the Indonesian city of Makassar on Sunday, The Jakarta Post reported citing police.
Churches have been targeted previously by extremists in Indonesia, the world's biggest Muslim-majority nation.
Ten hours after the attack near Katedral Church, police were still unable to identify any suspect.
At least 14 people were injured in a suspected suicide bombing outside a Church in the Indonesian port city of Makassar, capital of South Sulawesi province, on Sunday, police said.
The JAD, which is loyal to the Islamic State in Iraq and Syria, is linked with a group involved in a militant attack on Jolo, in the Philippines in 2018.
There has been no immediate claim of responsibility for the attack.
The attacks were carried out by a family of six, including two daughters aged 12 and 9, who were reportedly Islamic State sympathisizers and had recently returned from Syria.
Indonesia's deadliest militant attack took place on the tourist island of Bali in 2002, when bombers killed 202 people, a lot of them foreign tourists.
The attack came as Indonesia was on high alert following the arrest of Aris Sumarsono, known as Zulkarnaen, the leader of Jemmaah Islamiyah in December.