The lawyer said Israel started transferring 37 prisoners from the northern West Bank to Nafha jail in the desert of southern Israel on Wednesday.
Israeli authorities say the detainees are being moved so a section of Gilboa prison can be renovated to accommodate criminal prisoners, the lawyer said.
The prisoners object as their families will have to travel further to visit them, and insist any transfer must be to another jail in northern Israel.
They will return meals until Israel revokes the decision, and urged organizations and institutions to work to insist prisoners are held as close as possible to their hometowns, the lawyer added.
Under international law, it is illegal for Israel to detain Palestinians outside Palestinian territory.