What eats shrews?
Shrews are hunted by weasels, owls, and foxes. Not many animals eat shrew, supposedly they have a very bad taste.
Many owls eat shrews like the Barn Owl, Great Horned Owl, etc. Because they are in the rodent family, anything that normally eats small rodents will probably eat them. When disecting owl pellets you can find several skulls from them because when shrews are frightened they latch on to one another tails.
There are many inscetivorous mammals, including echidnas, opossums, small dasyurids, bilbies, all three kinds of moles, hedgehogs, shrews, solenodons, elephant shrews, treeshrews, bats, most primates, hyraxes (to some extent), armadillos, anteaters, pangolins, and tamanduas. One example is the Northern Short-Tailed Shrew.
Wolves eat all kinds of rabbits and so do owls. They both also eat shrews, hares, voles, muskrats, rats, mice, squirrels ,chipmunks and some types of birds. The costal owl eats fish and so do all wolves. But most other types of owls do not eat fish. I hopes this response helped you with your question.