Witnesses saw three men leave a package near the building in the west of the French capital.
Somebody noticed the package and moved it some ten metres (yards) away before fleeing, a source close to the enquiry said.
The bomb exploded minutes later at around 5.45am (0445 GMT) "an hour or so before people would be out on the streets," causing significant damage including blowing out windows within a 50-metre radius, the source said.
No group or individual immediately claimed responsibility for the attack.
Police and fire fighters were rushed to the area and sealed off the road where the blast occured.
In Jakarta, Teuku Faizasyah, Indonesian presidential spokesman on foreign affairs, said the government there had been informed of a bomb incident.
"But it's not clear whether it was only a bomb threat or a bomb explosion. We're still looking for clarity on whether we were the target or not," he added.
"I don't want to speculate, but there was a remote case in Paris before, which was a local issue. In the mid-2000s there was a case of a small bomb explosion at the Indonesian embassy in Paris. It turned out to be a local incident, and nothing to do with a national threat."
Coordinating Security Minister Djoko Suyanto told AFP: "This is being investigated by the Indonesian embassy in Paris with coordination with local authorities."
"The Indonesian ambassador in Paris reported that the explosion took place at one of the crossroads near the embassy at 5.20am. We don't know the target of the bomb. The ambassador is at the location but he can't go near.
"The windows were broken but there's no report yet of Indonesian or staff casualties. We are still waiting for developments," he added.