At least six people have been killed by the blasts, which hit several locations including a shopping centre.
Police say they believe more than a dozen attackers were involved. Some are still at large and have been exchanging fire with security forces.
President Joko Widodo has called for calm but condemned the “act of terror”.
“We all are grieving for the fallen victims of this incident, but we also condemn the act that has disturbed the security and peace and spread terror among our people,” he said.
There is no indication yet of who might be behind the assault. Indonesia has been attacked by Islamist militant groups in the past and was on high alert over the new year period after threats from the so-called Islamic State.
Images from the scene showed bodies lying on the road as well as seriously injured people being carried away. BBC Indonesian reporter, Jerome Wirawan, who is at the scene, said police had cordoned off the area.
Source:bbc.com