The first attack at the Santa Maria Roman Catholic church killed one person and wounded 11, police spokesman Frans Barung Mangera told TVOne network.
The large archipelago has seen a resurgence of Islamist militancy in recent months and years.
Shattered glass and chunks of concrete littered the entrance of the Santa Maria Church, which was sealed off by heavily armed police.
Elshinta radio, a local Indonesian broadcaster, has put the death toll at five but that information has yet to be confirmed by authorities.
The Islamic State (IS) group claimed responsibility for that incident although police rejected its involvement. The Islamic State group claimed responsibility.
The attacks come days after militant Islamist prisoners killed five members of an elite counter-terrorism force during a 36-hour stand-off at a high security jail on the outskirts of the capital, Jakarta.
Indonesia is the world's most populous Muslim country with more than 82% of its roughly 260,500,000 people following Islam. Inspector general Machfud Arifin told CNN Indonesia the suicide attack at St Mary's was carried out using a motorbike. Religious minorities, especially Christians, have been repeatedly targeted by militants. "We must leave it completely to the government to handle", the head of the Indonesian Communion of Churches said in a statement on Sunday quoted by The Jakarta Post.
Police officers have been deployed to the crime scenes to investigate and safeguard the areas, including members of Brimob and the bomb squad.
Improvised bombs disguised as Christmas gifts and delivered to churches and clergymen kill 19 people and injure scores more across Indonesia.
Investigators are on the alert, saying that the organization may be planning more attacks.