Not many animals eat shrew, supposedly they have a very bad taste.

Shrews are hunted by weasels, owls, and foxes. Shrews are capable of overpowering and killing the young of … A shrew will starve if it goes without food for more than a few hours. The shrew kills and eats whatever it can, with a variety of creatures included in its diet. This animal eats rabbits, shrews, squirrels, chipmunks and rats.

When they consume these prey, they have the possibility of contracting or carrying specific bacteria, parasites, or diseases that may be transmitted to humans through bites. Shrews will devour earthworms, bugs, insect larvae and eggs, snails, centipedes, millipedes and an array of invertebrates. As the name implies, insects make up a large portion of the typical shrew diet. Shrews need to consume 200 to 300% of their body weight in food each day in order to survive. Like all shrews, the Arctic shrew has a voracious and insatiable appetite due to its quick metabolism. Shrews eat everything from plants, mice, snakes, frogs, pigeons, salamanders, and even other shrews. The staples of the shrew diet are earthworms, arthropods, spiders, wood lice, snails, slugs, small rodents, worms and a large array of insects including beetles. The weasel is a carnivore. A shrew must eat every 2 to 3 hours to achieve this goal.

It eats insects, worms and small invertebrates, with a large proportion of its diet made up of larch sawflies, though Arctic shrews in captivity have been fed dead voles, fly pupae, and mealworms.

Although common shrews consume very high levels of invertebrates and other animal-based foods, they also occasionally eat some plant-based meals -- think conifer seeds, for example. They are also known to eat fish and frogs. Food habit studies have revealed that shrews eat beetles, grasshoppers, butterfly and moth larvae, ichneumonid wasps, crickets, spiders, snails, … The common shrew's carnivorous and insectivorous diet consists of insects, slugs, spiders, worms, amphibians and small rodents. Shrews are in the taxonomic order Insectivora.