Any food that is high in fiber and low in starch needs to be consumed with enough water in order to prevent constipation. Butternut squash is high in fiber, and for some babies this can cause constipation if they're not drinking enough water with their meals. However, if you provide your baby a balanced diet, that includes other foods that relieve constipation such as pears, or prunes, your child should not have a problem with constipation caused by butternut squash.