Jonathan Ben-Artzi, 19, has served seven months in a military jail after being given consecutive sentences of up to 31 days at a time. Army officials are now summoning him to appear at a court martial, which has harsher sentencing powers, on Tuesday.
Mr Ben-Artzi, who has been a pacifist since he was 12, will be among the first objectors to appear before a court martial. Last week Matan Kaminer, another refusenik, was also arraigned for court martial along with a third objector, Hagai Matar.
Mr Ben-Artzi's family believes that he is being singled out because of his connections. More than 170 objectors have been jailed since the start of the intifada.
The case has become a cause celebre in Israel because Mr Netanyahu's wife, Sara, is Mr Ben-Artzi's aunt and it may set a legal precedent regarding an individual's right to be exempted from military service in Israel.
Mr Ben-Artzi's lawyers plan to plead for his release on the grounds that he is a conscientious objector and should be exempt from compulsory military duty.
Conscientious objectors have a status that is recognised in international laws signed by Israel. "Because of my beliefs, my own country is going to imprison me, in defiance of international laws, basic moral values and fundamental human rights," Mr Ben-Artzi said in a statement to the Israeli Defence Force.
He said that he would be prepared to carry out alternative community service, such as teaching or helping the poor.
Asked whether his uncle, a former combat soldier in an elite commando unit, approved of his stand, Mr Ben-Artzi said: "He was prime minister and he knows that Israel is a democratic country. In a democracy there is respect for the principles of pacifism."
Mr Ben-Artzi's mother, Ofra, who lives in Jerusalem, demonstrated last week against the incarceration of her son outside the home of the chief military prosecutor, Menachem Finklestein with her husband, Matanya, and the parents of two other imprisoned conscientious objectors.
She said that the issue of her son's pacifism was raised during a family gathering a year ago, shortly before he was jailed for the first time. "His uncle just said: 'Oh maybe you'll change your mind'.
"Jonathan replied that in a democracy everyone has the right to ask another to change his mind. He is determined," she said.
Under Israeli conscription laws men are required to serve three years in the army and women two years. Although women can win exemption on the grounds of conscientious objection, men cannot - a difference that Mr Ben-Artzi's lawyers plan to exploit at the hearing in a military court in Jaffa.
Recent Israeli newspaper reports claim that the daughter of Israel's hardline chief of staff, Moshe Ya'alon, was recently exempted on the grounds of conscientious objection. Michael Sfard, a lawyer for Mr Ben-Artzi, said: "The army in Israel is a prestigious club that is run by secular men.
"While the army can tolerate exempting certain people who do not belong in the elite - women, people with mental problems, drug takers and so on - this case is different.
"This guy is a general example of a secular, middle-class recruit from a good family. When he says he does not belong to this club, this frightens them, so they are getting tough."
The army admitted recently that more than 20 per cent of 18-year-olds win exemption from duty on a number of grounds, which include claiming psychological problems.