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Children suffering from Autism Spectrum Disorder (ASD) have impaired social communication, interaction and restricted and repetitive behaviors. ASD is caused by abnormal brain developments which give rise to the behavioral characteristics associated with ASD. The clinical diagnosis of ASD is performed on the basis of behavioral assessment and it causes a time delay in early intervention, as there is a time gap between abnormal brain developments and associated behavioral characteristics. Electroencephalography (EEG) is a technique which measures the electrical activity produced by the brain and it has been used to detect several neurological disorders. Studies have shown that there is a variation in the EEG signals of a normal subject and EEG signals of ASD subjects. In this study, we obtained scalograms of EEG signals by using Continuous Wavelet Transform (CWT). Pre-trained deep Convolutional Neural Networks (CNNs) such as GoogLeNet, AlexNet, MobileNet and SqueezeNet were used for extracting the features from scalograms and classification of obtained scalograms from EEG signals of normal and ASD subjects. We also used Support Vector Machine (SVM) algorithm and Relevance Vector Machine (RVM) for classification of the features extracted by the deep CNNs. The GoogLeNet, AlexNet, MobileNet and SqueezeNet deep CNNs achieved a validation accuracy of 75%, 75.84%, 79.45% and 82.98% in classifying the scalograms generated from EEG signals. The SVM achieved an accuracy of 71.6%, 74.76%, 70.70% and 81.47% using GoogleNet, Mobilenet, AlexNet and SqueezeNet for scalogram feature extraction. The RVM achieved an accuracy of 65.5%, 69.9%, 65.3% and 72.59% when used for classification using the features generated from GoogLeNet, AlexNet, MobileNet and SqueezeNet.The SqueezeNet deep CNN performed better than GoogLeNet, AlexNet and MobileNet for classification of the EEG scalograms. The feature extraction using SqueezeNet also resulted in better classification accuracy obtained by SVM and RVM. The results indicate that pre-trained models can be used for classifying the ASD using scalograms of the EEG signals.