Visual private information leakage is an emerging key issue for the fast growing applications of video understanding like activity recognition. Existing approaches for mitigating privacy leakage in action recognition require privacy labels along with the action labels from the video dataset. However, annotating frames of video dataset for privacy labels is not feasible. Recent developments of self-supervised learning (SSL) have unleashed the untapped potential of the unlabeled data. For the first time, we present a novel training framework which removes privacy information from input video in a self-supervised manner without requiring privacy labels. Our training framework consists of three main components: anonymization function, self-supervised privacy removal branch, and action recognition branch. We train our framework using a minimax optimization strategy to minimize the action recognition cost function and maximize the privacy cost function through a contrastive self-supervised loss. Employing existing protocols of known-action and privacy attributes, our framework achieves a competitive action-privacy trade-off to the existing state-of-the-art supervised methods. In addition, we introduce a new protocol to evaluate the generalization of learned the anonymization function to novel-action and privacy attributes and show that our self-supervised framework outperforms existing supervised methods. Code available at: https://github.com/DAVEISHAN/SPAct