Pre-trained language models (PLMs) have demonstrated their exceptional performance across a wide range of natural language processing tasks. The utilization of PLM-based sentence embeddings enables the generation of contextual representations that capture rich semantic information. However, despite their success with unseen samples, current PLM-based representations suffer from poor robustness in adversarial scenarios. In this paper, we propose RobustEmbed, a self-supervised sentence embedding framework that enhances both generalization and robustness in various text representation tasks and against diverse adversarial attacks. By generating high-risk adversarial perturbations to promote higher invariance in the embedding space and leveraging the perturbation within a novel contrastive objective approach, RobustEmbed effectively learns high-quality sentence embeddings. Our extensive experiments validate the superiority of RobustEmbed over previous state-of-the-art self-supervised representations in adversarial settings, while also showcasing relative improvements in seven semantic textual similarity (STS) tasks and six transfer tasks. Specifically, our framework achieves a significant reduction in attack success rate from 75.51% to 39.62% for the BERTAttack attack technique, along with enhancements of 1.20% and 0.40% in STS tasks and transfer tasks, respectively.