Yes, researching and building are the jobs most likely to cause a villager to get injured. Farming, Healing and Breeding are safer!

bringing him to the food bin to eat will help, but it takes 5-8 "servings" before you may notice a difference in the health bar. But, nursing mothers and kids won't eat at the food bin, you just have to hope that they will eventually heal from village-wide feedings and nothing new weakens them further.