In multi-label text classification, each textual document can be assigned with one or more labels. Due to this nature, the multi-label text classification task is often considered to be more challenging compared to the binary or multi-class text classification problems. As an important task with broad applications in biomedicine such as assigning diagnosis codes, a number of different computational methods (e.g. training and combining binary classifiers for each label) have been proposed in recent years. However, many suffered from modest accuracy and efficiency, with only limited success in practical use. We propose ML-Net, a novel deep learning framework, for multi-label classification of biomedical texts. As an end-to-end system, ML-Net combines a label prediction network with an automated label count prediction mechanism to output an optimal set of labels by leveraging both predicted confidence score of each label and the contextual information in the target document. We evaluate ML-Net on three independent, publicly-available corpora in two kinds of text genres: biomedical literature and clinical notes. For evaluation, example-based measures such as precision, recall and f-measure are used. ML-Net is compared with several competitive machine learning baseline models. Our benchmarking results show that ML-Net compares favorably to the state-of-the-art methods in multi-label classification of biomedical texts. ML-NET is also shown to be robust when evaluated on different text genres in biomedicine. Unlike traditional machine learning methods, ML-Net does not require human efforts in feature engineering and is highly efficient and scalable approach to tasks with a large set of labels (no need to build individual classifiers for each separate label). Finally, ML-NET is able to dynamically estimate the label count based on the document context in a more systematic and accurate manner.