The female elephant was discovered in Sumatra's Way Kambas National Park on Monday.
Her trunk was broken off and she had five holes resembling gunshot wounds on the right side of her body, it said.
But no bullets were found inside the body, which officials suspect had been lying in the forest for at least two days.
"Its teeth were gone, maybe taken by hunters. So we assume she was shot because of that, but we still need to investigate more," environment ministry spokesman Djati Witjaksono Hadi told AFP.
The apparent killing of the elephant, believed to be about 20 years old, comes about two months after a pregnant elephant was found dead in a palm oil plantation in Sumatra.
The death was presumed to be the result of deliberate poisoning.
Also last year, authorities found a dead elephant without tusks in Aceh, along with its abandoned 11-month-old calf.
Sumatran elephants are listed as critically endangered animals by the International Union for the Conservation of Nature.
Massive deforestation for plantations has reduced their natural habitat and brought them into conflict with humans. Their tusks are also targets for poachers in the illegal ivory trade.
Way Kambas National Park is home to Sumatran elephants and also critically endangered Sumatran tigers, Sumatran rhinos and endangered Asian tapirs.
There are believed to be around 2,000 Sumatran elephants left in the wild.
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