The attack, which began with an attack near a Starbucks outlet, claimed two lives before security forces moved in. Police said one of the dead was a Canadian and one a police officer, without providing further details.
Islamic State of Iraq and the Levant quickly put out a claim of responsibility - a marked difference to the case of the most recent suicide bomb attack in Istanbul, which was attributed to the group but which it has still not admitted.
Indonesia has a long history of terrorist attacks on civilian targets, not least the Bali bombing of 2002, when 202 people were killed, many of them tourists.