My Side of the Mountain won critical plaudits upon its release. Numerous reviewers praised the novel for its detailed depiction of the wilderness and animals, its unsentimental treatment of animals and nature, and its characters, their maturation, and development. The New York Times in 1959 gave the novel a solid review, calling it "a delightful flight from civilization, written with real feeling for the woods." Children's author Zena Sutherland, writing in Children & Books at the time, called Sam's development from immature, impulsive child into a mature young adult "wholly convincing". Ruth Hill Viguers, reviewing the book in The Horn Book Magazine, concluded in 1959, "I believe it will be read year after year, linking together many generations in a chain of well-remembered joy and refreshment."
In addition to being named to the Newbery Award Honors list, the book was also an American Library Association's Notable Book for 1959, was placed on the Hans Christian Andersen Award 1959 honors list, was given a Lewis Carroll Shelf Award citation (in 1965), and won the 1959 George G. Stone Center for Children's Books Award.
The book continues to be praised in the 1990s and 2000s. Book critic Eden Ross Lipson included it in her 2000 list of the best children's books, and said it "skillfully blends themes of nature, courage, curiosity, and independence". Librarians and authors Janice DeLong and Rachel Schwedt listed the book as one of a "core collection" of novels all libraries should have in their young-adult fiction section. Author Rafael Yglesias, writing in the New York Times in 1990, called it "vividly realized", and full of "clean realism, fascinating detail and economical suspense". He declared it "a contemporary classic". Author Charles Wohlforth, writing in 2004, agreed that it was a classic of contemporary children's literature. By 1998, the book had been translated into numerous foreign languages, and visitors to the Cannon Free Library in Delhi, New York, often asked to see the abandoned farm where the novel was set. (The abandoned farm does not actually exist; the Gribley farm is entirely fictional.)
The book has not always won uncritical praise. In 1999, reviewer Mary Harris Russell noted that "the narrator, Sam, speaks with a tone more measured than that of most teenagers. That tone grates on some readers."
Robert F. Kennedy, Jr. has cited My Side of the Mountain with inspiring him to become a falconer, which led him into a career in environmental law and environmental activism. Television host and pet advice author Marc Morrone and award-winning natural history author Ken Lamberton also credit the book with generating their interest in falconry.
Based on a 2007 online poll, the National Education Association named the book one of its "Teachers' Top 100 Books for Children." It was one of the "Top 100 Chapter Books" of all time in a 2012 poll by School Library Journal.