The blast occurred around 7:00 am local time (1200 GMT) as military and police personnel were taking a morning jog around the leafy grounds in the centre of the capital.
“We’re now investigating why the smoke grenade was there,” Jakarta police chief Gatot Eddy told reporters, adding that the two injured had been rushed to the hospital.
“One of them was wounded on the hand and the other was injured on the leg,” he said.
There is a military barracks on the grounds of the national monument.
Gatot said there was no indication of an attack.
Jakarta military chief Eko Margiyono also stressed that there was no indication that the explosion was anything but an accident.
“This wasn’t something extraordinary,” he added.
Indonesia, the world’s biggest Muslim majority nation, has long struggled with Islamist militancy and has suffered regular attacks.
In October, Indonesian President Joko Widodo ordered beefed-up security after two militants from a terror group stabbed his chief security minister.
He survived the attack, which led to the arrests of dozens of suspects.
