I think cherry trees are a popular food among the larva of swallowtail butterflies (image: [url]https://www.megkazul.net/butterflies/display.php?image=swallowtail06.jpg[/url]) and the larva of other butterflies. I've never seen a tree die because of caterpillars, even when all of the leaves are eaten, so I think the tree will be fine. The larva of butterflies are very fickle about what they eat and will not hurt any other plant in your yard. You will probably not notice them on the plant because they roam on it individually (unlike moth larva which form huge community nests). Moth larva are less picky about what they eat and might damage other plants as well.
Is the tree native to your area or did you buy it from a nursery? I would be surprised if caterpillars were eating a non-native tree. I don't think the mother butterfly would lay eggs on a plant she'd never seen before because she couldn't be sure if the larva would like it or not.
If I'm wrong and it's not caterpillars causing the damage, maybe you should follow my friend's advice; I had a similar problem and a friend of mine told me to treat the tree with fungicide. Apparently aphids and other small parasites don't like this treatment and will leave the tree if you put fungicide on it. I'm not sure why.