Yes, it's a complete sentence. "He has to eat" would itself be a complete sentence, with "more" just a simple adverb to modify how his eating habits should change. A similar example:
She has to study more (if she wants to get better grades).
It's not necessary to specify what she should study. "More" by itself implies the general "more often", or "for longer periods of time", or even "more assiduously".
Of course it's also possible to specify exactly what he should eat more of, which as you say would modify the defined noun:
The doctor said he has to eat more fruit and vegetables.