Old English scrincan "to draw in the limbs, contract, shrivel up; wither, pine away" (class III strong verb; past tense scranc, past participle scruncen), from Proto-Germanic *skrink- (cf. Middle Dutch schrinken), probably from PIE root *(s)ker- (3) "to turn, bend."
Originally with causal shrench (cf. drink/drench). Sense of "become reduced in size" recorded from late 13c. The meaning "draw back, recoil" (early 14c.) perhaps was suggested by the behavior of snails. Transitive sense, "cause to shrink" is from late 14c. Shrink-wrap is attested from 1961 (shrinking-wrap from 1959). Shrinking violet "shy person" attested from 1882.