While humans can solve a visual puzzle that requires logical reasoning by observing only few samples, it would require training over a large number of samples for state-of-the-art deep reasoning models to obtain similar performance on the same task. In this work, we propose to solve such a few-shot (or low-shot) abstract visual reasoning problem by resorting to \emph{analogical reasoning}, which is a unique human ability to identify structural or relational similarity between two sets. Specifically, we construct analogical and non-analogical training pairs of two different problem instances, e.g., the latter is created by perturbing or shuffling the original (former) problem. Then, we extract the structural relations among elements in both domains in a pair by enforcing analogical ones to be as similar as possible, while minimizing similarities between non-analogical ones. This analogical contrastive learning allows to effectively learn the relational representations of given abstract reasoning tasks. We validate our method on RAVEN dataset, on which it outperforms state-of-the-art method, with larger gains when the training data is scarce. We further meta-learn our analogical contrastive learning model over the same tasks with diverse attributes, and show that it generalizes to the same visual reasoning problem with unseen attributes.