Injured pigeon

Hello Julia, you say pigeon but not sure if you mean feral (rock pigeon) or woodpigeon type. Pigeons naturally spend a lot of time on the ground foraging for food, drinking water, etc., What makes you think it is injured ? have you seen a wound or just the fact it is spending a lot of time on the ground ? If the latter then I would say if it is able to potter around just leave it and keep an eye on it from distance, they do spend much of their time wandering around on the ground and if it is not visibly injured then it should be fine.