Early identification of respiratory irregularities is critical for improving lung health and reducing global mortality rates. The analysis of respiratory sounds plays a significant role in characterizing the respiratory system’s condition and identifying abnormalities. The main contribution of this study is to investigate the performance when the input data, represented by cochleogram, is used to feed the Vision Transformer (ViT) architecture, since this input–classifier combination is the first time it has been applied to adventitious sound classification to our knowledge. Although ViT has shown promising results in audio classification tasks by applying self-attention to spectrogram patches, we extend this approach by applying the cochleogram, which captures specific spectro-temporal features of adventitious sounds. The proposed methodology is evaluated on the ICBHI dataset. We compare the classification performance of ViT with other state-of-the-art CNN approaches using spectrogram, Mel frequency cepstral coefficients, constant-Q transform, and cochleogram as input data. Our results confirm the superior classification performance combining cochleogram and ViT, highlighting the potential of ViT for reliable respiratory sound classification. This study contributes to the ongoing efforts in developing automatic intelligent techniques with the aim to significantly augment the speed and effectiveness of respiratory disease detection, thereby addressing a critical need in the medical field.