Medical images may contain various types of artifacts with different patterns and mixtures, which depend on many factors such as scan setting, machine condition, patients' characteristics, surrounding environment, etc. However, existing deep-learning-based artifact reduction methods are restricted by their training set with specific predetermined artifact types and patterns. As such, they have limited clinical adoption. In this paper, we introduce One-Shot medical image Artifact Reduction (OSAR), which exploits the power of deep learning but without using pre-trained general networks. Specifically, we train a light-weight image-specific artifact reduction network using data synthesized from the input image at test-time. Without requiring any prior large training data set, OSAR can work with almost any medical images that contain varying additive artifacts which are not in any existing data sets. In addition, Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are used as vehicles and show that the proposed method can reduce artifacts better than state-of-the-art both qualitatively and quantitatively using shorter test time.