Issa Qaraqe, head of prisoners affairs for the Palestinian Authority, said that "around 1,300 Palestinian prisoners" were participating in the hunger strike and the number could rise.
The Palestinian Prisoners Club NGO put the number at 1,500.
Israeli prison service spokesman Assaf Librati said that 700 prisoners had announced on Sunday their intention to begin a hunger strike.
Barghouti is serving a life sentence over his role in the violent second Palestinian intifada. He is a popular figure, with polls suggesting he could win the Palestinian presidency.
The strike was called in connection with Palestinian Prisoners Day, which is observed annually.
Some 6,500 Palestinians are currently detained by Israel.