1748, "place where shrubs are planted," from shrub + -ery. As "shrubs collectively," from 1777. Shrubbage is from 1713.
Entries linking to shrubbery
shrub n.
"low-growing bush, a woody plant with stems branched from or near the ground," Middle English shrubbe, from Old English scrybb "brushwood, shrubbery," a rare and late word (but preserved also, perhaps, in Shrewsbury), possibly from a Scandinavian source (compare dialectal Danish skrub "brushwood," Norwegian skrubba "dwarf tree"). OED says it is presumably related to North Frisian skrobb "broom plant, brushwood;" West Flemish schrobbe "climbing wild pea," with a base notion of "rough plant." Watkins has this as ultimately from PIE *(s)kerb-, an extended form of root *sker- (1) "to cut."
The line which divides trees from shrubs is to a large extent arbitrary, and is often very unsatisfactory in application, but in general the name shrub may be applied to a woody plant of less size than a tree, with several permanent woody stems dividing from the bottom, more slender and lower than in a tree. [Century Dictionary]
-ery
word-forming element making nouns meaning "place for, art of, condition of, quantity of," from Middle English -erie, from Latin -arius (see -ary). Also sometimes in modern colloquial use "the collectivity of" or "an example of."