The rising need for swift response times makes it essential to use computing resources and network capacities efficiently at the edges of the networks. Mobile Edge Computing (MEC) handles this by processing user data near where it is generated rather than always relying on remote cloud centres. Yet, scheduling tasks under these conditions can be difficult because workloads shift, resources vary, and network performance is unstable. Traditional scheduling strategies often underperform in such rapidly changing settings, and even Deep Reinforcement Learning (DRL) solutions usually require extensive retraining whenever they encounter unfamiliar tasks. This paper proposes a self-supervised DRL framework for zero-shot task scheduling in MEC environments. The system integrates self-supervised learning to generate task embeddings, enabling the model to classify tasks into clusters based on resource requirements and execution complexity. A Soft Actor-Critic (SAC)-based scheduler then optimally assigns tasks to MEC nodes while dynamically adapting to network conditions. The training process combines contrastive learning for task representation and policy optimization to enhance scheduling decisions. Simulations demonstrate that the proposed approach reduces task completion time by up to 22 %, lowers energy consumption by 29 %, and improves latency by 18 % over baseline methods.