Such anxiety is called separation anxiety. It is not within the norm for a child of ten to experience such acute anxiety. You can reassure her, but try not to make too large an issue of it - that will likely only make matters worse. If the reaction does not interfere with normal day-today activities, you really needn't do much about it. However, if it interferes with your daughter's life at home or in school, you should have her evaluated by a pediatric mental health clinician.
I have a 9 year old, I think as they get older they realize the world is not all roses. I think maybe she saw something on Tv or heard something in school and it makes her think god, that could happen to my mom, try asking her about it and see what she says.