With the rapid growth of the global drone market, a variety of small drones have posed a certain threat to public safety. Therefore, we need to detect small drones in a timely manner so as to take effective countermeasures. At present, the method based on deep learning has made a great breakthrough in the field of target detection, but it is not good at detecting small drones. In order to solve the above problems, we proposed the IRSDD-YOLOv5 model, which is based on the current advanced detector YOLOv5. Firstly, in the feature extraction stage, we designed an infrared small target detection module (IRSTDM) suitable for the infrared recognition of small drones, which extracted and retained the target details to allow IRSDD-YOLOv5 to effectively detect small targets. Secondly, in the target prediction stage, we used the small target prediction head (PH) to complete the prediction of the prior information output via the infrared small target detection module (IRSTDM). We optimized the loss function by calculating the distance between the true box and the predicted box to improve the detection performance of the algorithm. In addition, we constructed a single-frame infrared drone detection dataset (SIDD), annotated at pixel level, and published an SIDD dataset publicly. According to some real scenes of drone invasion, we divided four scenes in the dataset: the city, sky, mountain and sea. We used mainstream instance segmentation algorithms (Blendmask, BoxInst, etc.) to train and evaluate the performances of the four parts of the dataset, respectively. The experimental results show that the proposed algorithm demonstrates good performance. The AP50 measurements of IRSDD-YOLOv5 in the mountain scene and ocean scene reached peak values of 79.8% and 93.4%, respectively, which are increases of 3.8% and 4% compared with YOLOv5. We also made a theoretical analysis of the detection accuracy of different scenarios in the dataset.