Sometimes, yes. While children often exchange germs and parasites (like common colds or hair lice), schools and daycare centers must still act appropriately to keep all children safe. For example, if one child spikes a fever, they are isolated in a nursing office or sent home, and lice checks are performed after an outbreak to contain the spread.
However, if your child gets food poisoning from undercooked cafeteria food, that illness could be considered an injury. This is because there was a failure in the duty of care, and a wholly preventable harm was caused because of that failure.