Lachanophobia means “fear of vegetables”.
Language Notes
This is a modern word, invented from the Greek words “λάχάνον”, meaning “vegetable” (or really anything cultivated in a garden, as opposed to collected from the wild) and φόβος , meaning fear, terror, flight or dismay.
As it’s an invented word, there’s nothing to say that you can’t be both more creative and exact in defining your child’s specific fear by sticking Latin or Greek-sounding words on at the end, such as, say, Lachanophobia Brusselus Sproutus, Lachanophobia tomatitis or Lachanophobia cucumi sativi.