The importance of a good hearing function to preserve memory and cognitive abilities has been shown in the adult population, but studies on the pediatric population are currently lacking. This study aims at evaluating the effects of a bone-anchored hearing implant (BAHI) on speech perception, speech processing, and memory abilities in children with single side deafness (SSD). We enrolled n = 25 children with SSD and assessed them prior to BAHI implantation, and at 1-month and 3-month follow-ups after BAHI implantation using tests of perception in silence and perception in phonemic confusion, dictation in silence and noise, and working memory and short-term memory function in conditions of silence and noise. We also enrolled and evaluated n = 15 children with normal hearing. We found a statistically significant difference in performance between healthy children and children with SSD before BAHI implantation in the scores of all tests. After 3 months from BAHI implantation, the performance of children with SSD was comparable to that of healthy subjects as assessed by tests of speech perception, working memory, and short-term memory function in silence condition, while differences persisted in the scores of the dictation test (both in silence and noise conditions) and of the working memory function test in noise condition. Our data suggest that in children with SSD BAHI improves speech perception and memory. Speech rehabilitation may be necessary to further improve speech processing.