Barghouti's call for the strike has given it added credibility, with the 57-year-old serving five life sentences over his role in the violent second Palestinian intifada.
In the NYT piece, Barghouti accused Israel of conducting "mass arbitrary arrests and ill-treatment of Palestinian prisoners", and said that a hunger strike is "the most peaceful form of resistance available" against these abuses.
"After consultations with prisoners of various factions, PPP-affiliated prisoners chose to join the battle for freedom and dignity on April 17, which coincides with Palestinian Prisoner's Day".
Fares said hundreds of prisoners launched a 28-day strike in 2012.
And, in 2014, 800 prisoners staged a strike against administrative detention for 63 days before a reaching a deal with the Israeli prison authorities and deciding to end their strike.
The PPCS called on the global community to shoulder its legal and moral responsibilities and pressure Israel to stop its ongoing crimes against the Palestinian prisoners.
It comes in protest of the inhumane detention conditions that Palestinian prisoners continue to face.
Throughout the op-ed, Barghouti only vaguely alludes to the reason he is in prison.
"The strike is a decision of the prisoners". Officially, the inmates are demanding that Israeli authorities allow more visits from family members and access to telephones.
A recent report from UK-based rights group Amnesty International also condemned Israel's policy of holding Palestinian prisoners inside Israel, describing it as "unlawful and cruel". One cage held two Palestinians in Israeli prison uniform.
About 6,500 Palestinians are now detained by Israel on a wide range of offenses and alleged crimes.
The Public Security Ministry said that the IPS would not conduct negotiations with the prisoners, in accordance with prison policy, and that all prisoners participating in a hunger strike will receive immediate disciplinary measures.
"Instead of saying to him - as a responsible newspaper should - that if he doesn't have a shred of evidence to support his stories then they can't be published, The New York Times published them in its opinion pages and didn't even bother to explain to its readers that the author is a convicted murderer of the worst kind", Lapid wrote.
The last large-scale hunger strike was in February 2013, when 3,000 Palestinians refused to eat for one day to protest against the death of a fellow detainee.
A spokesman for the Israel Prison Service (IPS), Assaf Librati, said the prison service does not, as a rule, negotiate with prisoners.
For Palestinians, the prisons have become a stark symbol of Israel's occupation. Palestinians consider brethren held in Israeli jails as national heroes.