Dataset distillation aims to optimize a small set so that a model trained on the set achieves performance similar to that of a model trained on the full dataset. While many supervised methods have achieved remarkable success in distilling a large dataset into a small set of representative samples, however, they are not designed to produce a distilled dataset that can be effectively used to facilitate self-supervised pre-training. To this end, we propose a novel problem of distilling an unlabeled dataset into a set of small synthetic samples for efficient self-supervised learning (SSL). We first prove that a gradient of synthetic samples with respect to a SSL objective in naive bilevel optimization is \textit{biased} due to the randomness originating from data augmentations or masking for inner optimization. To address this issue, we propose to minimize the mean squared error (MSE) between a model's representations of the synthetic examples and their corresponding learnable target feature representations for the inner objective, which does not introduce any randomness. Our primary motivation is that the model obtained by the proposed inner optimization can mimic the \textit{self-supervised target model}. To achieve this, we also introduce the MSE between representations of the inner model and the self-supervised target model on the original full dataset for outer optimization. We empirically validate the effectiveness of our method on transfer learning. Our code is available at https://github.com/db-Lee/selfsup_dd