Human pose estimation (HPE) has become essential in numerous applications including healthcare, activity recognition, and human-computer interaction. However, the privacy implications of processing sensitive visual data present significant deployment barriers in critical domains. While traditional anonymization techniques offer limited protection and often compromise data utility for broader motion analysis, Differential Privacy (DP) provides formal privacy guarantees but typically degrades model performance when applied naively. In this work, we present the first comprehensive framework for differentially private 2D human pose estimation (2D-HPE) by applying Differentially Private Stochastic Gradient Descent (DP-SGD) to this task. To effectively balance privacy with performance, we adopt Projected DP-SGD (PDP-SGD), which projects the noisy gradients to a low-dimensional subspace. Next, we incorporate Feature Differential Privacy(FDP) to selectively privatize only sensitive features while retaining public visual cues. Finally, we propose a hybrid feature-projective DP framework that combines both approaches to balance privacy and accuracy for HPE. We evaluate our approach on the MPII dataset across varying privacy budgets, training strategies, and clipping norms. Our combined feature-projective method consistently outperforms vanilla DP-SGD and individual baselines, achieving up to 82.61\% mean PCKh@0.5 at $ε= 0.8$, substantially closing the gap to the non-private performance. This work lays foundation for privacy-preserving human pose estimation in real-world, sensitive applications.