- The Mildred L. Batchelder Award (1973) for "One More River"
- The Edgar Allan Poe Award (1974) for "The Indian in the Cupboard"
- The Christopher Award (1979) for "The Farthest-Away Mountain"
- The Guardian Children's Fiction Prize (1981) for "The Backward Shadow"
- The Eleanor Farjeon Award (1987) for her contribution to children's literature
- The British Book Awards Children's Book of the Year (1991) for "Broken Bridge"
- The Phoenix Award (2005) for "One More River"
- The Costa Book Awards Children's Book Award (2010) for "The L-Shaped Room"
In addition to these awards, Banks has also been nominated for several other awards, including the Hans Christian Andersen Award, the Newbery Medal, and the National Book Award.