late 14c., "low, stunted tree," variant of shrobbe (see shrub), perhaps influenced by a Scandinavian word (such as Danish dialectal skrub "a stunted tree, brushwood"). Collective sense "brush, shrubs" is attested from 1805. As an adjective from 1710. Scrub oak recorded from 1766.
Transferred sense of "mean, insignificant fellow" is from 1580s; U.S. sports meaning "athlete not on the varsity team" is recorded from 1892, probably from this, but compare scrub "hard-working servant, drudge" (1709), perhaps from influence of scrub (v.).