Background: The perception of basic emotional sounds, such as crying and laughter is associated with effective interpersonal communication. Difficulties with the perception and analysis of sounds that complicate understanding emotions at an early development age may contribute to communication deficits. Methods: This study focused on auditory nonverbal emotional perception including emotional vocalizations with opposite valences (crying and laughter) and neutral sound (phoneme “Pᴂ”). We conducted event-related potential analysis and compared peak alpha frequencies (PAFs) for different conditions in children with autism spectrum disorder (ASD) and typically developing (TD) children aged 4 to 6 years old (N = 25 for each group). Results: Children with ASD had a higher amplitude of P100 and lower amplitude of N200 for all types of sounds and higher P270 in response to neutral phoneme. During the perception of emotional sounds, children with ASD demonstrated a single P270 electroencephalography (EEG) component instead of a P200–P300 complex specific to TD children. However, the most significant differences were associated with a response to emotional valences of stimuli. The EEG differences between crying and laughter were expressed as a lower amplitude of N400 and higher PAF for crying compared to laughter and were found only in TD children. Conclusions: Children with ASD have shown not just abnormal acoustical perception but altered emotional analysis of affective sounds as well.