The low-intensity blast happened at the Ekayana Buddhist Centre this evening, police said.
Local media reported the device went off inside next to a glass door but had caused little damage. A second device emitted smoke but failed to explode, national police chief detective Sutarman said.
Neither police nor the centre said who may have been behind the blasts.
There has been growing anger in Indonesia, which has the world's biggest Muslim population, at the plight of the Rohingya Muslim minority in Buddhist-majority Myanmar.
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"They were placed at a glass door, which was broken." However, the centre said in a statement that there was "no damage at all".
National police spokesman Ronny Sompie added that the blast "injured one person, who sustained an abrasion to the hand".
Police, including members of the bomb squad and the elite counter-terror unit, were at the scene, he said.
The temple, one of the biggest in Jakarta, said it hoped the blasts would "not cause any unrest in the religious community".
Several outbreaks of violence between Buddhists and Muslims in Myanmar have tempered international optimism about the country's dramatic political reforms as it emerges from decades of military rule.