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]

WordNet (r) 3.0 (2006):

herbaceous
    adj 1: characteristic of a nonwoody herb or plant part