Sumatran elephants are on the brink of extinction with only about 2,400-2,800 left in the world, according to the World Wide Fund for Nature.
Weighing about 78 kilograms (172 pounds), the calf was born at Way Kambas National Park in the nation's southern Sumatra, the Ministry of Environment and Forestry said.
It was born at an elephant centre inside the national park at around 10 am local time (0300 GMT), the ministry said in a statement. The gender was not given.
The health of the calf and its mother was being monitored by park staff.
A male elephant was born at the same national park this month, to a different mother and in good health, the second such birth this year.
On Saturday, a critically endangered Sumatran rhino was born at the same national park. Less than 80 are estimated to be left in the world.
"Good news comes to us one after another," Indonesian environment minister Siti Nurbaya Bakar said in the statement.
"This good news should encourage us Indonesians to continue the conservation efforts of protected species in the country."
The elephant population is threatened by rampant poaching for their tusks, which are prized in the illegal wildlife trade.
The archipelago nation faces an ongoing battle against wildlife crime and several elephant poisoning cases have been reported in recent years.
Deforestation has reduced the critically endangered elephants' natural habitat and brought them into increasing conflict with humans.
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