Automatic diagnosis systems aim to probe for symptoms (i.e., symptom checking) and diagnose disease through multi-turn conversations with patients. Most previous works formulate it as a sequential decision process and use reinforcement learning (RL) to decide whether to inquire about symptoms or make a diagnosis. However, these RL-based methods heavily rely on the elaborate reward function and usually suffer from an unstable training process and low data efficiency. In this work, we propose an effective multi-task framework for automatic diagnosis called MTDiag. We first reformulate symptom checking as a multi-label classification task by direct supervision. Each medical dialogue is equivalently converted into multiple samples for classification, which can also help alleviate the data scarcity problem. Furthermore, we design a multi-task learning strategy to guide the symptom checking procedure with disease information and further utilize contrastive learning to better distinguish symptoms between diseases. Extensive experimental results show that our method achieves state-of-the-art performance on four public datasets with 1.7%~3.1% improvement in disease diagnosis, demonstrating the superiority of the proposed method. Additionally, our model is now deployed in an online medical consultant system as an assistant tool for real-life doctors.