Sergeant Victor Isasi, 42, died of piercing injuries caused by the deer’s antlers, the military stated. The deer, which is one of several animals kept in the gardens, attacked Mr Isasi at dawn.
The animal was a gift to the presidential residence, according to the Ministry of the Environment.
An infantry spokesman said it was usually kept in a separate area with other wild animals which are not supposed to come in contact with people.
CCTV captured the moment the soldier approached the deer before the fatal incident.
Military spokesman Colonel Victor Urdapilleta said the soldier “died from a perforation in the thorax”.
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In previous administrations these have included ostriches and ponies.
The animal was a chital from India, the Director of Wildlife at the Ministry of the Environment, Frederick Bauer, told local media.
The chital, which is also known as spotted deer and native to the Indian subcontinent, is kept in the ten hectare (24 acre) gardens of President Mario Abdo Benitez’s, 50, official residence near the capital of Asuncion.
Mr Bauer said the chital was part of a litter from a government ranch and admitted: “It is not appropriate to have exotic animals in captivity but there is no regulation.”
Mr Urdapilleta said the officials responsible for the gardens had consulted with the environment ministry before introducing the deer.
The grounds mostly host native species such as rheas, macaws and an mborevi, Mr Urdapilleta revealed.