In a rare statement, the humanitarian organization criticized what it called a "systemic suspension" of visits by Israeli authorities as a punishment for the striking prisoners, in violation of international law.
The ICRC says that "families are paying the price for this situation."
The strike reached its 17th day on Wednesday. The prisoners seek better conditions, including more family visits.
Israel Prison Service spokesman Assaf Librati says about 850 prisoners are still taking part in the strike. He denied claims Israel is violating international law, but didn't elaborate.
In the West Bank town of Ramallah, thousands of Palestinians are attending a solidarity rally for the prisoners.