Four vehicles were damaged but no staff were injured as the office was closed at the time.
The attack was the second on a foreign aid agency in North West Frontier Province this week.
"Something was thrown inside the ICRC compound in Peshawar and damaged four vehicles and some property, but caused no injuries or fatalities," Raza Hamdani, Red Cross spokesman, told Reuters on Saturday.
Iftikhar Khan, the city's police chief, said the incident was being investigated.
On Monday, a grenade was thrown at a compound of the US-based Save the Children aid group in Battagram, wounding two Pakistani employees.
Aid agencies in the area are working in the many large refugee camps housing people from neighbouring Afghanistan, and helping communities recovering from an earthquake in 2005.
On Monday, a grenade was thrown at a compound of the US-based Save the Children aid group in Battagram, wounding two Pakistani employees.
Aid agencies in the area are working in the many large refugee camps housing people from neighbouring Afghanistan, and helping communities recovering from an earthquake in 2005.
