Haaretz identified the Israeli trooper as a 31-year-old Army reservist, Yaniv Mazor.
He was sentenced to 20 days in prison last week for refusing to join the Israeli Army, saying he is protesting Tel Aviv's occupation of the Palestinian territories.
Mazor went on hunger strike the day after his incarceration. He has told his lawyer that his protest move has nothing to do with his imprisonment.
The development comes on the heels of the large-scale hunger strikes staged by Palestinian prisoners over the recent months.
An estimated 1,600 to 2,500 Palestinian prisoners went on hunger strike on April 17 to protest against Israel’s administrative detention rules, the use of solitary confinement, maltreatment of sick detainees, and difficulty in securing family visits and strip searches that are imposed on visitors.
The prisoners ended their hunger strike on May 14 after Israeli prison authorities bowed to their demand for better confinement conditions. Palestinian footballer Mahmud Sarsak and two other prisoners, however, refused to eat and are still on hunger strike, urging to be released immediately.
Administrative detention is a controversial practice used by Tel Aviv, which allows Israeli authorities to hold people, mostly Palestinians, without charge or trial for up to six months. The imprisonment is renewable indefinitely.
An Israeli draft dodger has reportedly stopped eating in a military prison in, what has been described as, a show of solidarity with Palestinian administrative detainees.