1590s, "stunted, inferior, shabby;" see scrub (n.1) + -y (2). In reference to land, "covered with brush or underwood," from 1670s. Related: Scrubbiness.
Entries linking to scrubby
scrub n.1
late 14c., "a low, stunted tree; a shrub," variant of shrobbe, from Old English scrybb, scrub (see shrub, which is the common form of the same word), perhaps influenced by a cognate Scandinavian word (such as Danish dialectal skrub, Old Danish skrubbe, "a stunted tree, brushwood").
The collective sense of "brush, stunted trees, shrubs; a tract of these" is attested by 1805. Transferred sense of "mean, insignificant fellow" is from 1580s; earlier it meant a small breed of cattle (1550s). The U.S. sports meaning "athlete not on the varsity team" is recorded from 1892, probably from this "insignificant" sense, but compare scrub "hard-working servant, drudge" (1709), which is perhaps from influence of scrub (v.).
As an adjective from 1710, "of inferior breed or stunted growth," from the noun. Scrub oak for a kind of low American species, is recorded from 1766.
-y 2
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy). Adjectives such as hugy, vasty are artificial words that exist for the sake of poetical metrics.