"like a box in shape," 1858, from box (n.1) + -y (2). Related: Boxiness.
Entries linking to boxy
box n.1
"rectangular wooden container," usually with a lid, Old English box, also the name of a type of shrub, from Late Latin buxis, from Greek pyxis "boxwood," pyxion "writing table, box," made of boxwood, from pyxos "box tree," which is of uncertain origin. Beekes suggests a loan-word from Italy, as that is where the tree is native. Dutch bus, German Büchse "box; barrel of a gun," also are Latin loan-words.
The meaning "compartment at a theater" is from c. 1600 (box seat in the theatrical sense is by 1850). The meaning "pigeon-hole at a post office" is from 1832. The meaning "television" is from 1950 (earlier "gramophone player," 1924). The meaning "station of a player in baseball" is from 1881. The graphics sense of "space enclosed within borders and rules" is from 1929. The slang meaning "vulva" is attested 17c., according to "Dictionary of American Slang;" modern use seems to date from c. World War II, perhaps originally Australian, on the notion of box of tricks. Box lunch (n.) is attested from 1899. The box set "multiple-album, CD or cassette issue of the work of an artist" is attested by 1955. To think or act outside the box "contrary to convention" is attested by 1994.
-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.