The drought is adding to the devastation caused by Cyclone Pam six months ago, with people in some parts forced to forage for food in the bush.
Dr Jacob Kool from the World Health Organisation's office in Vanuatu said the girl from Tanna Island died from severe diarrhoea, which may have been caused by contaminated water or inedible food.
"There is a severe food shortage on the island," he said.
"People have been eating unusual food crops which they don't normally eat.
"Some people say diarrhoea is caused by that.