One of the main limitations in the field of audio signal processing is the lack of large public datasets with audio representations and high-quality annotations due to restrictions of copyrighted commercial music. We present Melon Playlist Dataset, a public dataset of mel-spectrograms for 649,091 tracks and 148,826 associated playlists annotated by 30,652 different tags. All the data is gathered from Melon, a popular Korean streaming service. The dataset is suitable for music information retrieval tasks, in particular, auto-tagging and automatic playlist continuation. Even though the latter can be addressed by collaborative filtering approaches, audio provides opportunities for research on track suggestions and building systems resistant to the cold-start problem, for which we provide a baseline. Moreover, the playlists and the annotations included in the Melon Playlist Dataset make it suitable for metric learning and representation learning.