One of the currently assumed causes of impaired social interaction exhibited by children with autism spectrum disorders (ASD) is dysfunction of the mirror neuron system (MNS), which is responsible for imitation, understanding the intentions and emotions of other people. Desynchronization of sensorimotor rhythms is considered to be the indicator of MNS activation. This study aimed to analyze the specific patterns of reactivity of the μ-rhythm in an individually determined frequency range and β-rhythm on the EEG in children with ASD during independent movements, observation, imitation and auditory perception of similar movements performed by another person. The data collected were compared to those describing normally developing children. The study involved right-handed children with ASD aged 5–10 (n = 10) and normally developing children (n = 10). In the independent movements exercise, β-rhythm desynchronization was more pronounced in children with ASD, with difference becoming significant in the P4 locus (p = 0.03). In the movements imitation exercise, the groups showed significant differences in the EEG μ-rhythm in the locus C3 (p = 0.03). Auditory perception of movements revealed significant differences in the ranges of both μ-rhythm (loci F3 and Fz (p = 0.02), F4 (p = 0.04), Cz (p = 0.009)) and β-rhythm (loci Fz (p = 0.01), F4 (p = 0.02)). In these situations, children with ASD exhibited synchronization of sensorimotor rhythms, while normally developing children showed desynchronization. The assumption is that the specific patterns revealed are the consequences of disruption of functions of MNS and anti-mirror system. The data obtained can be used in development of EEG biofeedback training protocols for children with ASD.