Gunmen open fire at West Bank Red Cross office
The shooting attack took place at 11pm at the ICRC's Hebron office, with bullets striking a vehicle, gate, and main building.
"Our staff are physically unharmed. None of them were on site at the time the shooting incident took place," the ICRC said in a statement.
"The incident is, however, destabilising for our entire team."
The Red Cross said it had no information about who carried out the attack.
"We call for unconditional support and respect for our strictly neutral and impartial work," the humanitarian body added.
Since 1969, the International Committee of the Red Cross (ICRC) has been responsible for facilitating family visits for prisoners' relatives from the West Bank and Gaza, without any financial or logistical assistance from Israel.
Prisoners' relatives are heavily dependent on the agency, but frustrations about the organisation's inability to pressure Israel to ease restrictions on prisoners has led to angry protests outside Red Cross offices in the occupied West Bank.
In February, the Gaza offices of the ICRC were briefly closed following protests were held to support imprisoned journalist Mohammed al-Qiq.
Demonstrators said the group was not doing enough to intervene on behalf of the detainee who was on hunger strike.
Last summer saw frequent protests break out outside the ICRC offices in East Jerusalem and the West Bank after the group reduced the number of family visits for male Palestinian prisoners.