Potatoes are used in Red Army Training, the opening level of Call of Duty 2. They are grenade substitutes used by the player and his fellow comrades to practice throwing grenades. This is surely due to the fact that the Soviet Union's war industry was still very slow to start off in this early state of the German invasion of the USSR. Being nothing more than a normal potato, it does not cause any damage, nor explode like more conventional hand grenades. If thrown at another character, it will harmlessly bounce off without the NPC reacting at all.
If the player throws a potato at a German soldier in the level Red Army Training, the German will be surprised and confused, and say "Kartoffeln?" which is German for 'potatoes.' Also, if the player throws enough at the German, a potato will get stuck in his head.
Although potatoes are much cheaper than real hand grenades, it is still strange to waste food in a grenade training since the USSR was in time of crisis.
In Call of Duty 4: Modern Warfare, a box of potatoes can be seen inside the weapons room in the level "F.N.G".
So far this is, and probably will always, be the only edible weapon in the whole Call of Duty series.