1713, "act or fact of shrinking, contraction of a material to a smaller surface or bulk," from shrink (v.) + -age. The meaning "amount by which something has shrunk" is by 1862.
Entries linking to shrinkage
shrink v.
Middle English shrinken, from Old English scrincan "to draw in the limbs, contract spontaneously, shrivel up; wither (through death, age, disease, etc.), pine away" (class III strong verb; past tense scranc, past participle scruncen), from Proto-Germanic *skrink- (source also of Middle Dutch schrinken, Swedish skrynka "to wrinkle"), probably from PIE root *sker- (2) "to turn, bend."
Originally it had a causal form, shrench (compare drink/drench). The sense of "become reduced in size" is recorded from late 13c. The meaning "draw back, recoil" (early 14c.) often was in reference to the behavior of snails; the meaning "flinch, wince, draw back from fear or shame" is by mid-14c. The transitive sense of "cause to shrink, make to appear smaller" is from late 14c.
Shrink-wrap "clingy thin plastic film" used in food packaging is attested from 1961 (shrinking-wrap is by 1959). Shrinking violet "shy person" is attested by 1882.
-age
word-forming element in nouns of act, process, function, condition, from Old French and French -age, from Late Latin -aticum "belonging to, related to," originally neuter adjectival suffix, from PIE *-at- (source of Latin -atus, past participle suffix of verbs of the first conjugation) + *-(i)ko-, secondary suffix forming adjectives (see -ic).