Unsupervised sentence embeddings learning has been recently dominated by contrastive learning methods (e.g., SimCSE), which keep positive pairs similar and push negative pairs apart. The contrast operation aims to keep as much information as possible by maximizing the mutual information between positive instances, which leads to redundant information in sentence embedding. To address this problem, we present an information minimization based contrastive learning InforMin-CL model to retain the useful information and discard the redundant information by maximizing the mutual information and minimizing the information entropy between positive instances meanwhile for unsupervised sentence representation learning. Specifically, we find that information minimization can be achieved by simple contrast and reconstruction objectives. The reconstruction operation reconstitutes the positive instance via the other positive instance to minimize the information entropy between positive instances. We evaluate our model on fourteen downstream tasks, including both supervised and unsupervised (semantic textual similarity) tasks. Extensive experimental results show that our InforMin-CL obtains a state-of-the-art performance.