|Northern Short-tailed Shrew.|
Shrewd derives from adding -ed to the Middle English shrewe, meaning a wicked man. The origin of the noun shrew, referring to the species of small insectivorous mammals, is unclear. The Old English word for shrew-mouse is screawa. The word is otherwise unknown outside English. One theory suggests that screawa derives from the Proto-Germanic *skraw-, meaning to cut or a cutting tool. The shrew has a very pointed snout which might have reminded people of a cutting tool. (Yes, I know what you're thinking and I agree. That's a bit of a stretch.) The idea of a shrew as a spiteful, vexatious woman came about in the late fourteenth century, developing from the earlier sense of a shrew as a spiteful person (male or female). Some species of shrew (the animal, not the people) are venomous, which is highly unusual among mammals. Tradition suggests the animal has a malignant influence and was viewed with superstitious dread.
The first association of shrewd with cunning is from the 1510s. Modern usage has dropped most of the negative connotations of shrewd, although the term shrew for an an ill-tempered, scolding woman is still alive and well. I suspect William Shakespeare's The Taming of the Shrew has contributed to that meaning's longevity. However, a shrewd person is considered to be wily and crafty—words with a shady undertone—so maybe the negative connotation lingers on.