The Collaborative International Dictionary of English v.0.48:

nonwoody \nonwoody\ adj.
   not woody; not consisting of or resembling wood; as, nonwoody
   plants. Opposite of woody. [Narrower terms: herbaceous;
   pulpy, fleshy]
   [WordNet 1.5]

The Collaborative International Dictionary of English v.0.48:

Herbaceous \Her*ba"ceous\, a. [L. herbaceus grassy. See Herb.]
   Of or pertaining to herbs; having the nature, texture, or
   characteristics, of an herb; as, herbaceous plants; an
   herbaceous stem.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

25 Moby Thesaurus words for "herbaceous":
   botanic, bulbous, cereal, farinaceous, fruitlike, fruity, herbal,
   herbose, herbous, herby, leguminose, leguminous, plantlike,
   radicated, radiciform, radicular, rhizoid, rootlike, tuberous,
   vegetable, vegetal, vegetarian, vegetational, vegetative, weedy