The blasts were close to a shopping centre, the Sarinah, where victims' bodies were seen strewn on the ground.
At least six explosions rang out and a police post was damaged. "This is a bomb," Anton Charliyan, national police spokesman told AFP.
He warned people to stay away, saying police fear there could be more bombs. The shooting was happening outside a Starbucks opposite the shopping centre.
It was not immediately clear who was behind the attacks.
After a series of attacks on foreigners in the last decade, Indonesian extremists have in recent years directed their violence at domestic "enemies of Islam", mostly police.
There have been no attacks against foreigners since the 2009 twin hotel bombings in Jakarta which killed seven people.//Agence France Presse