Auditory cortex in each hemisphere shows preference to sounds from the opposite hemifield in the auditory space. Besides this contralateral dominance, the auditory cortex shows functional and structural lateralization, presumably influencing the features of subsequent auditory processing. Children have been shown to differ from adults in the hemispheric balance of activation in higher-order auditory based tasks. We studied, first, whether the contralateral dominance can be detected in 7- to 8-year-old children and, second, whether the response properties of auditory cortex in children differ between hemispheres. Magnetoencephalography (MEG) responses to simple tones revealed adult-like contralateral preference that was, however, extended in time in children. Moreover, we found stronger emphasis towards mature response properties in the right than left hemisphere, pointing to faster maturation of the right-hemisphere auditory cortex. The activation strength of the child-typical prolonged response was significantly decreased with age, within the narrow age-range of the studied child population. Our results demonstrate that although the spatial sensitivity to the opposite hemifield has emerged by 7 years of age, the population-level neurophysiological response shows salient immature features, manifested particularly in the left hemisphere. The observed functional differences between hemispheres may influence higher-level processing stages, for example, in language function.