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.
Also Read
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.
There are believed to be around 2,000 Sumatran elephants left in the wild.
Disclaimer: No Business Standard Journalist was involved in creation of this content