The soldiers, from the feared Duvdevan Unit, were charged with animal cruelty and firearms offences after a video of the incident surfaced.
Filmed by one of the men, the clip shows the off-duty pair driving past a camel by a sand dune near the Dead Sea while one of them fires at the helpless animal.
According to the Times of Israel, the soldier who fired the shot was sentenced to four months while the comrade who filmed it was jailed for two months. Both have reportedly been demoted to the rank of private.
As the bullet hits the unsuspecting camel - which later died - hysterical laughter can be heard coming from the car.
At a preliminary hearing, the soldier who fired the fatal shot was asked about the laughter and admitted: 'We were in a kind of euphoria. It was exciting.'
The incident took place in November while the two men - now suspended from duty - were on leave before they began officer training in the commando unit.
An Israeli army spokesman said: 'This was a serious incident that does not meet the standards expected from IDF [Israel Defence Force] soldiers.'
Lawyers for the pair acknowledge the severity of the incident, but said they should be credited for confessing their actions.
The Duvdevan Unit, part of Israel's West Bank is one of the most feared throughout the Middle East and often works as an undercover plain clothes squad fighting terrorism.
Etti Altman - chair of the Israeli animal rights group Let the Animals Live had called for lengthy jail sentences saying: 'Where did their compassion go, the mercy toward defenseless creatures?'
(Daily Mail - Jan 29, 2016)
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